Representing logical and semantic structure of knowledge acquired from discourse

COGNITIVE PSYCHOLOGY 7, 371-458 (1975)

Representing Logical and Semantic Structure

of Knowledge Acquired from Discourse

CARL H. FREDERIKSEN

University of California, Berkeley

A network model of logical and semantic structures from which speakers or writers generate linguistic messages at the discourse level is presented. While linguistic structures were considered in developing the model, the semantic and logical networks are defined without reference to linguistic structures and thus may be used to represent knowledge structures acquired from both linguistic and nonlinguistic sources. A second problem addressed is that of determining what logical and semantic information is acquired when a text is understood. To assess acquired knowledge, a procedure is presented for coding a subject’s verbal recon- struction of knowledge acquired from a presented text (or other input) against the logical and semantic structure from which the text (or other input) was derived. The procedures are illustrated using data obtained from children who were asked to “retell” simple narrative stories.

The process of linguistic communication can be characterized in terms of five stages. First, a speaker or writer selects from his store of conceptual knowledge (or semantic memory) some organized set of information for transmission. Second, the speaker or writer encodes the conceptual message into a string of well-formed natural language productions. The third stage involves the physical transmission and reception of these natural language productions, either through speech or written text. The fourth stage occurs when a listener or reader transforms the natural language productions actually received into some semantic form or conceptual message. Finally, the listener or reader incorporates the interpreted semantic information into his semantic memory or general store of knowledge. Understanding, then, may be regarded as a process whereby a listener or reader attempts to infer the knowledge structure of a speaker or writer by using the available linguistic message, contextual information, and his own knowledge store as “data structures” from which the inference is to be made.

A complete account of the communication process will have to start with a description of the knowledge structure from which a text is

This research was supported by grant number OEG-0-9-140396-4497 (010) from the Com- mittee on Basic Research in Education, National Academy of Sciences, and by grant number GS-4023 from the National Science Foundation.

Requests for reprints should be sent to Carl H. Frederiksen, Department of Psychology, University of California, Berkeley, CA 94720.

371 Copyright 0 1975 by Academic Press, Inc. All rights of reproduction in any form reserved.

372 CARL H. FREDERIKSEN

derived and a description of the semantic information which constitutes a listener’s or reader’s understanding of a text. While processes which generate text from semantic structures (processes of linguistic production) may be quite different from those which generate semantic structures from linguistic productions (comprehension processes), a necessary prerequisite to an understanding of either process is an ability to specify semantic structures-both as underlying structures from which texts are generated and as representations of knowledge acquired from texts.

If a detailed model of logical and semantic structures were available, it could be used as a basis for assessing subjects’ memory structures for text, either by providing a basis for systematically probing subjects’ memories for text, or as a reference structure against which subjects’ text recalls (or other verbal responses) could be scored. It then would be possible to assess precisely what semantic information a subject has acquired from a text and to specify what relationship obtains between semantic information acquired from a text and the semantic information from which the text was derived. Thus, by comparing a subject’s memory structure for a text (as inferred from his responses to probes or text recall) to the logical and semantic structure from which the text was generated, it ought to be possible to begin to reconstruct the processing operations which a subject applied to an input text to generate his memory structure for the text. In this manner, one could begin to determine precisely what logical and semantic knowledge is acquired when a text is “understood,” specify the processes by which such knowledge is acquired, and by systematically constructing texts from specified semantic and logical structures study effects of structural characteristics of texts on these processes.

The present paper is concerned with presenting an explicit model of knowledge structure. The model may be regarded as representing memory structures from which speakers (or writers) can generate linguistic messages at the discourse level. The model which will be presented will be defined entirely without reference to linguistic structures, although numerous sentence examples will be given to illustrate semantic structures. Thus, the model is capable of representing the informational structure of nonlinguistic “messages” such as visual arrays and experienced events as well as that coded in linguistic messages. The model represents both semantic structures consisting of propositions which are represented as networks of concepts connected by labeled binary relations and which identify events or states, and logical structures consisting of networks of propositions which are connected by various labeled logical, causal, and algebraic relations. A second purpose of this paper is to present a procedure for coding logical and semantic informa-

REPRESENTING KNOWLEDGE STRUCTURE 373

tion acquired from text which is based on the logical and semantic structures developed in the first part of the paper.

Our purposes, then, in developing a model of memory structures underlying text are both theoretical and methodological. The development of a solution to the methodological problem, the assessment of semantic information which is acquired when a text is understood, is directly related to and dependent on the development of a theoretical model of logical and semantic structures in human long-term memory. The methodological problem thus motivates on practical grounds the theoretical development. It should not be surprising that there is such a close relationship between a theoretical and a measurement problem when the measurement problem involves coding responses consisting of free verbal protocols (cf. Newell & Simon, 1971; Waterman & Newell, 1971).

Semantic structures have recently come to be regarded as central to linguistic descriptions of natural language productions. Until relatively recently, linguists influenced by Chomsky, had tended to restrict their attention to the sentence as the largest unit of analysis and had empha- sized syntax at the expense of semantics in representing sentence structure. Criticisms of these two aspects of Chomsky’s theory, the emphasis on syntax and the adoption of the sentence as the unit of analysis, have led to a new emphasis on semantics and on discourse as the unit of analysis,

Generative semanticists such as McCawley (1968) and Lakoff (1971a, b) have come to believe that there is no formal difference between so- called syntactic and semantic rules; rather there are only semantic representations and grammatical transformations relating them to surface structures (sentences). It has seemed to them that it would be more parsimonious to adopt a system of grammar which starts with logical predi- cates and contains rules for mapping these propositions directly onto surface sentences.

Many linguists have criticized taking the sentence as the primary unit of analysis and defining the grammaticality of a sentence without reference to the context in which a sentence occurs. They have pointed out that certain derivations of a sentence may be judged to be ill-formed in one context and grammatical in another. Thus, speakers apparently have an ability to make judgments of grammaticality which reflect the context in which a sentence occurs. Therefore, any linguistic theory which attempts to define grammaticality in isolation from context will be an inad- equate model of speakers’ competence. This realization has led many linguists to give increased attention to effects of context. In this work, attention has been given to: (1) the conceptual context of an utterance: the presuppositions (beliefs or intentions) held by a speaker at the time of an utterance (Kartunnen, 1968, 1971, 1974; Keenan, 1971); (2) the


extra-linguistic context: the time, place, and location of speaker and hearer (Fillmore, 1966, 1971; Leech, 1969); and (3) the linguistic context: the context given by previous discourse within which a sentence is embedded (Halliday, 1970; Chafe, 1974). The importance of these contextu- alization factors as well as the claim that speakers’ competence (ability to judge grammaticality) pertains to texts and not only to sentences, has led some linguists to propose considering the text as the unit of analysis (Sanders, 1969; Grimes, 1975) and to attempt to develop text grammars (Van Dijk, 1973; G&tad, 1973). A text grammar would not only have to be capable of generating individual sentences within a discourse, it would also have to be capable of generating these sentences relative to the context of previous discourse.

The conception of linguistic productions which seems to be emerging appears to be much more plausible as a basis for a psychological model of linguistic production than was Chomsky’s system of grammar. The conception seems to have the following characteristics. First, the basis for linguistic productions is semantic (propositional) structures. Second, grammatical rules are being formulated at the discourse level, relative to discourse context, extra-linguistic context, and conceptual context. Third, grammatical rules are being formulated as transformations which map directly from semantic structures to surface sentences. To be complete, then, a linguistic description of text will have to consist of two components: a semantic structure and a set of grammatical rules which generate texts from semantic structures.

There have been a number of attempts in linguistics (Chafe, 1970; Leech, 1969; Grimes, 1974), computational linguistics (Simmons, 1972, 1973), artificial intelligence (Schank, 1972) and psychology (Kintsch, 1972; Rumelhart, Lindsay & Norman, 1972; Crothers, 1973) to specify semantic structures. Of these, only the work of Crothers and Grimes appears to have been explicity concerned with specifying semantic structures applicable to linguistic messages at the discourse level. Many of these models have adopted the general notion of a semantic network, a concatenation of labeled binary relations which connect semantic “concepts.” Systems differ in the types of concepts which are connected into networks, and in the types of elementary semantic relations which connect concepts into higher-order semantic units. Most systems allow for “embedding” by allowing that a concept itself may be replaced by a relational structure (or “proposition”). In certain of these models, binary relations corresponding to Fillmore’s (1968, 1971) case categories are defined (e.g., Simmons, 1972, 1973; Chafe, 1970; Grimes, 1974; Rumelhart et al., 1972). Leech (1969) has explicitly adopted a dimensional structure into his system in order to represent relations of relative time and location. Simmons and Bruce (1971) have demonstrated the


equivalence of semantic network and propositional notations by presenting an algorithm for converting their semantic network representations into simple propositions of a first-order predicate calculus.

Systems also differ in their treatment of “concepts” corresponding to lexical items (i.e., content words). Thus, Schank (1972, 1973) analyzes lexical concepts into structures composed of more “primitive” concepts and semantic relations, while Simmons (1973) tends to leave lexical concepts intact. Wilks (1973) has commented on this difference, suggesting that it results from a difference in objectives. If one’s purpose is to design a system capable of paraphrasing or translating, one may adopt a level of semantic analysis more like that of Simmons; if one’s purpose is to design a question-answering system with extensive reasoning capabili- ties, then one would adopt a system more like Schank’s. From a psychological standpoint, it may be reasonable to suppose that lexical items in most cases represent reasonably intact “concepts” which a subject does not ordinarily “unpack,” but that subjects are capable of ex- panding the meanings of lexical concepts when required to do so by the demands of a particular task.

Semantic networks frequently have been represented as data structures in computer programs (e.g., Simmons, 1973; Frijda, 1972). Compu- tationally, semantic networks so represented can be viewed as functions or procedures to be executed. For example, semantic relations can “be defined as generating functions that would produce an appropriate syntactic structure corresponding to each semantic relation and its argu- ments” (Simmons, 1973; p. 78). The significance of this observation is that it has extended the notion of a static semantic memory to include active procedural information. Thus, there need not be any formal distinction between data structures and procedures operating on them and it is possible to formulate memory models which include stored “procedural” information as well as “structural” information.

The semantic structure which will be developed in the present paper incorporates a number of ideas developed by previous investigators. The model initially grew out of an attempt to extend Simmons’ (1972) sentence-based semantic network to represent semantic and logical information underlying texts consisting of many sentences. The goal was to defme a network which was sufficiently general that it could be used as a basis for coding subjects’ text recalls. The present semantic structures begin with a taxonomy of objects and actions similar to that suggested by Chafe (1970). The part of the system which specifies causal circum- stances and participants in events is built around “case” relations which derive from Fillmore’s (1968, 1971) case categories and Chafe’s (1970) “relations of nouns to verbs.” The treatment of derived forms is based on Chafe’s (1970) discussion of derivation. The dimensional structure


developed in the present system is based on Leech’s (1969) treatment of relative time and location; and the treatment of tense and aspect in the present system reflects Leech’s work on the subject. The semantic network system of notation was adopted from Simmons (1972) and Schank (1972) and the notion of (possibly empty) “slots” connected by labeled binary relations was adopted from Schank (1972, 1973). Two other sources unrelated to linguistics also influenced the development of the present model. One is the treatment of metric data structures in psychological measurement theory (cf. Coombs, 1964; Tversky, 1969). The other is Rescher’s (1964) treatment of counter-factual conditional propositions and Simon and Rescher’s (1966) paper on “cause and counterfactual.” Further reference to these sources will be made as the relevant topics are introduced.

The logical and semantic structures which will be presented have a number of aspects which distinguish the present network model from other semantic network models. First, the system is well-defined in the sense that every relation specified in the system is explicitly defined without reference to linguistic productions. Definitions consist of restrictions on the two slots connected by a relation and a definition of the relation connecting the two slots. Second, the model consists of two network structures: (1) a semantic structure or semantic network consisting of a collection of labeled binary relations which represent events or states and which connect slots containing (in most cases) concepts; and (2) a logical structure or logical network consisting of a collection of labeled binary logical, causal or algebraic relations connecting propositions which are represented as substructures in the semantic network. Third, the model considers in detail the algebraic (and metric) properties of “noncase” (i.e., classificatory, attributive, degree, temporal, locative, and quantifier) relations and defines certain relations having specified algebraic properties (re: transitivity, symmetry, and reflexivity) which may be used to connect propositions containing these noncase relations. What results is a mechanism for representing comparative relations, and relations of relative time and location, tense and aspect. Fourth, the present system contains a stochastic (or probabilistic) element, representing the fact that speakers (or writers) are often uncertain, and hence imprecise, in expressing semantic information involving metric values. They are also often imprecise in specifying case and other nonmetric information. Such uncertainty is often expressed by qualifying propositions with “hedges” such as may and might. Uncertainty of this latter sort is treated in the present system as uncertainty about the truth value of a proposition and is represented in the system by means of qualifying operators on the truth value of a proposition defined by a concept-relation-concept triple. Finally, the system distinguishes between “symbolic” and “nonsymbolic” objects, and “cognitive” and


“noncognitive” actions, both of which involve symbolic content; and develops relations which specify the content of symbolic objects or cognitive (symbolic) actions.

The remainder of the paper is organized into the following sections. The tirst section outlines the main elements of the model, starting with classification of objects and actions and then identifying all case relations and noncase relations which are used to specify events or states in the semantic structure. Numerous examples are included to illustrate the relations. The second section develops detailed definitions and network notation for all relations in the semantic structure. The third section develops detailed definitions and network notation for relations in the logical structure. Included in this section are logical and causal relations, and algebraic (order and proximity) relations which are used to represent relative or comparative information. The use of order and proximity relations to represent relative information is illustrated with structural representations of comparatives, relative time, and relative location. Tense and aspect operators are also defined in this section in terms of their underlying structural representations. Also, in this section operators are defined which, when applied to a relation, operate on the truth-value of a proposition given by a relation and its two connected slots. Modal operators are also defined in this section. In the final section, the use of the above structures to develop logical and semantic networks underlying discourse is discussed and illustrated with examples. The use of network structures to code semantic and logical information acquired from text is illustrated using data obtained from children who were asked to “retell” simple narrative stories. The entire system is summarized in a series of figures and tables.

MAIN ELEMENTS OF THE MODEL

A semantic network consists of two sorts of elements: concepts which are represented as “nodes” in the network, and labeled binary relations which connect pairs of concepts. A concatenation of concept-relation- concept triples defines a semantic network. The set of all concepts which occur as nodes in a semantic network defines the content of the network. If all of the concepts are removed from a network leaving only empty “slots” in their places, what remains is the structure of the network minus the content. Thus, it is convenient to speak of two sorts of information: conceptual information and structural information. If a text is regarded as derived from a semantic network, then the text may be thought of as conveying both conceptual information which is coded in the text by means of a set of content words, and structural information which is coded in the text by means of a grammar which generates an ordered string of content words plus syntactic markers.

A semantic network can be defined by specifying a set of concepts


and defining a set of labeled binary relations which connect the concepts. If the network is to have general applicability as a model of memory structures from which speakers (or writers) generate English texts, then the set of concepts will have to include every concept which is lex- icalized in English, and the set of labeled relations will have to reflect every relation which could hold between concept pairs. Definitions of relations also will have to include restrictions on the types of concepts which they can connect. For example, in A canary is a bird, the relation “is a subset of” can only connect pairs of physical objects. A natural starting point, then, in defining a semantic network is to develop a taxonomy of concepts. Relations can then be defined which connect restricted classes of concepts, classes which correspond to classes of concepts identified in the taxonomy. In fact, the classification of actions and objects with which we begin will be found to determine many aspects of the systems of relations which follow.

In the present system, we begin with two classes of concepts: objects and actions. Objects are defined as things which occupy space, the defining feature being “having a location in space” (marked as [+location] in Fig. 1). Actions are defined as things which occupy a position or interval of time and involve change. The defining features for actions, then, are [+time] and [+change] (Fig. 2). Features such as [+location], [+time], and [fchange] in most cases will be regarded as unanalyzed primitives in our system. In general, the notation [+feature] means that the feature is a defining feature for a class of concepts, [-feature] means that absence of the feature is a defining property of the class of concepts, and features which are not marked under a class of concepts are not defining features for that conceptual class.

Figure 1 presents the classification of objects. The figure contains a hierarchical tree diagram depicting (as one moves from left to right in the tree) the classification of objects into subclasses. In the tree, branching occurs at three levels and thus generates five main classes of objects. The numbers which occur after each terminal branch refer to the num- bered examples in Fig. 1. The same conventions will be adopted in figures subsequent to Fig. 1. The first branch in the tree represents a classification of objects into two major subclasses: static objects andprocessive objects, the distinguishing feature being [+change]. Processive objects are characterized by a process, i.e., are constantly undergoing change, while static objects are characterized by the absence of change. Ex- amples of processive objects are (nouns) animal, dance, and wind; examples of static objects are book and rock. Processive objects are further subdivided into animate objects which are living things capable of initiating change [ +animate], and inanimate processive objects which are not animate [-animate]. Plants are regarded as inanimate processive objects because, while they are characterized by a process (as are all liv-

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ing things), they are not capable of initiating change. Processive objects such as wind and&z are classified as inanimate because they are not living and cannot initiate change. Finally, inanimate processive objects and static objects can be either symbolic (examples (2) and (4)) or nonsymbolic (examples (3) and (5)). A symbolic object consists of a set of symbols which represent its meaning or semantic content. For example, a book is a static physical object which consists of a set of symbols representing the book’s semantic content. The feature [+theme] is used to denote the relation “having semantic content.”

The classification of actions is summarized in Fig. 2. The first branch in the hierarchy of actions specifies two major subclasses of actions: resultive actions and processes. Processes are actions which do not produce a change in a state or other process (marked [-result] in Fig. 2); resultive actions are actions which produce a change in a state or a process, i.e., a result (marked [+result] in Fig. 2). Examples of processes are: breathe, walk, play, know, and feel; examples of resultive actions are: break (entails a physical change in an object), go (somewhere; entails a change in location of a physical object), write (something; a cre- ative act resulting in a physical object), and learn (something; entails a change in a cognitive state from not knowing to knowing something).

The second level of branching in Fig. 2 involves a distinction between physical and cognitive actions. Consider first resultive actions. Physical resultive actions are distinguished by the feature [+physical] which indicates that the action results in a physical change involving an object. A physical action can result either in a symbolic object (terminal branch (2), see Fig. 2, example (2)) or in a state or process involving an object which is not symbolic (terminal branch (1); see Fig. 2, example (1)). Cognitive resultive actions do not result in a physical change; rather they result in a change involving a cognitive process (see example (3)). Turning to processes, a physical process is an action involving a process of physical change in an object; while a cognitive process is an action involving a process which is not physical but which has a thematic content associated with it. Cognitive processes refer to such processes as knowing, experiencing, feeling, and believing while physical processes refer to such processes as breathing, sleeping, walking, and burning. Some processes are both physical and cognitive: e.g., play (baseball), and act (a part), both of which are physical activities which are also cognitive.

The final level of branching involves processes only. Processes can be either simple: involving only one object or class of objects; or relative: involving a second object or class of objects. Examples of simple and relative cognitive processes are: feel (happy; simple), feel (an object; relative), understand (about something; simple), and understand (someone;

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relative). For examples of simple and relative physical processes, see examples (4)-(7) in Fig. 2.

In addition to a set of objects and actions, a semantic network also consists of a set of relations which connect objects and actions to other concepts, thus defining “states” and “events.” A state consists of an object or object class together with a set of stative relations which identify the object or class of objects, thus distinguishing it from other classes of objects. An event consists of an action or class of actions together with a set of relations which are of two types: case relations and identifying relations. Case relations specify a causal system involving an action; identifying relations distinguish an action or class of actions from other classes of actions. The remainder of this section will be concerned with classifying the relations which are employed in the present system to specify states and events. The classification of relations will be presented in the same manner as it was presented for concepts: by means of hierarchial tree diagrams. The terminal branches of the trees represent the relations defined in the system. Immediately following each terminal branch is a label which is used to denote the relation in the semantic network and a number which corresponds to a num- bered example accompanying the figure. Explicit definitions of each relation and network notation will be presented in later sections. The in- tent here is merely to indicate what relations are used to define the semantic network. We will begin with case relations, considering first case relations involving resultive actions and then case relations involving processes. We will then consider in turn: stative relations, the degree relation, relations identifying actions, and relations of location and time.

Case relations. A resultive action is an action which produces a change in a state or process. Hence, specifying an event involving a resultive action involves specifying a causal system associated with the event,, a system which includes the resulting state or process. Figure 3 identifies the immediate structural components of the causal system associated with a resultive action. The system consists of an immediate cause of the action which can be either animate (agent: AGT) or inanimate (inanimate. agent: I-AGT); an instrument (INST) which may be used to carry out the action; animate or inanimate objects which are immediately affected by the action (affected objects: DATl (“dative”) for animate objects and OBJl for inanimate objects); the state or process existing immediately prior to the action (SOURCE); the state or process existing immediately after the action (RESULT); and, if the action has an immediate cause which is animate, there may be a future state or process towards which the action is directed (GOAL). Since an event involving a resultive action may occur as a part of a causal sequence con-


AGENT ACT (1) [+animatel

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FIG. 3. Case relations: resultive actions. Examples: (1) The mnn (AGT) broke the window. The child (AGT) learned the alphabet. The WZQII (AGT) wrote a letter. (2) The wind (I-AGT) broke the window. (3) The man broke the window with a bat (INST). The man wrote a letter wifh a pen (INST). (4) The man gave John (DATl) the bat (OBJl). The man killed the bear (DATl). (5) The man broke the window (OBJl). (6) The man walked from the door (SOURCE: a stative proposition specifying the man’s location immediately prior to the action). (7) The man walked to the gate (RESULT: a stative proposition specifying the man’s location immediately following the action). (8) The man wrote a book about China (RESULT: a symbolic object). (9) The child learned the alphabet. viz., The child learned and as a result the child knows the alphabet (RESULT: a proposition containing a cognitive process).) (10) The man broke the window to rep&e the cracked glass (GOAL: a proposition specifying a future event involving the window).

taining the event as a part of the sequence, the causal system represented by case relations, i.e., the “case system” or “case frame,” is restricted to the immediate cause, to objects immediately affected by the action, to the immediate result of the action, etc. The term “immediate”


signifies that there is no other cause, affected object, result, etc., which intervenes between (respectively) the immediate cause and the action, between the action and the immediate affected object, between the action and the immediate result, etc. Sentence examples of each case relation may be found in Fig. 3. Observe that the distinctions which were made involving resultive actions, i.e., between physical and cognitive actions, and between symbolic and nonsymbolic results, occur as different classes of results of an action (examples (7)-(9)). Thus, a nonsymbolic physical result is a state or physical process (e.g., the man walked to the gate, a stative result; the man made the motor run, a processive result); a symbolic physical result is a symbolic object (example (8): write a book); and a cognitive result is a cognitive process (example (9)). The RESULT relation will later be defined as connecting a resultive action and a “slot” containing a proposition representing a state or event. The SOURCE and GOAL relations correspondly connect propositions to a resultive action. Thus slots associated with these case relations contain embedded semantic structures.

The case system associated with a process is much simpler than that associated with a resultive action (see Fig. 4). If a process is a simple physical process, its case system involves only a processive object which is undergoing physical change associated with the process, here referred to as the patient (following Chafe’s (1970) terminology). A patient may be an animate object (PAT) or an inanimate processive object (I-PAT). Examples are: The man breathes (Fig. 4, example (1)) and The fire burns (Fig. 4, example (2)). Some processive objects are very closely related to processes (e.g.,fire, burn). In these cases, the processive object represents the patient in the case frame for the process, and the process represents the action associated with the case frame. Many processes also occur as resultive actions. For example, The man walks is an event associated with a process, but (see Fig. 3, example (7)) The man walked to the gate is an event associated with a resultive action: the action involved produces a change of state involving the man’s location. The case system for simple cognitive processes involves an animate patient (PAT) and a relation specifying the symbolic content of the cognitive process (THEME2). Examples are (Fig. 4, example (6)) The man knows Italian (where Italian refers to the content of the man’s knowledge) and John feels happy. The theme “slot” can contain an entire proposition as in The king believed that the world is flat. A process also can be both physical and cognitive (Fig. 4, example (6)) as in The boy plays baseball. If a case system associated with a process contains an animate patient, then it can also contain a goal: a future state or event towards which a process is directed (GOAL; see Fig. 4, example (5)). Finally, a process may be relative, i.e., it may involve an object or


-PATIENT --I ANIMATE I+animatel

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DATZ (3)

0852 (4)

GOAL2 (5)

THEME2 (6)

FIG. 4. Case relations: processes. Examples: (1) The man (PAT) breathes. The man (PAT) knows Italian. The boy (PAT) plays baseball. (2) The$re (I-PAT) burns. The wind (I-PAT) blows. The plant (I-PAT) grows. (3) The man (PAT) rides the horse (DAT2). John (PAT) likes Alice (DATZ). (4) The man (PAT) drives the car (OBJ2). The fire (I-PAT) bums the wood (OBJ2). (5) The man (PAT) jogs to lose weight (GOALZ: a stative proposition specifying the man’s weight relative to his weight at the time at which he jogs). (6) The man (PAT) knows Ifaliun (THEME2). John (PAT) feels happy (THEME2). The boy plays baseball (THEME2). The King (PAT) believed that the world is flat (THEME2: a stative proposition).

object set other than the patient. Such an object is called the related object of a process and may be animate (DAT2) or inanimate (OBJ2). A related object, unlike an affected object in the case of a resultive action, is not necessarily affected by the process. Examples of related objects are given in Fig. 4, examples (3) and (4).

Stative relations. An object which occupies a “slot” in a case system may have associated with it stative relations which distinguish the object from other objects or object classes. An object together with any stative relations associated with the object will be referred to as the “state system” associated with the object. The classification of stative relations which specify a state system for an object or object set is presented in Figs. 5 and 6. A state system identifies an object or object set by means of a number of classes of relations which are identified by the first level of branching in Figs. 5 and 6. Thus, a stative relation may specify that an object (or each member of a set of objects) has associated with it another


object (or object set) which is a part of the object (the HASP relation; example (1)). It may specify that an object set contains another object set as a subset, or that the object set is a subset of a larger class of objects (class$catory relations). It may specify that an object or object set has associated with it an attribute (attributive relations); that an object or object set has a spatial location (locative relations); or location in time (temporal relations). If an object is symbolic, a stative relation may specify the symbolic content of the object (the THEME1 relation, Fig. 5, example (11)). Finally, stative relations include relations which determine and quantify a countable object set (determiner and quantifier relations: Fig. 6). Altogether, stative relations define a state system which specifies how an object set is determined and quantified, its location in space and time, its attributes, its content (if it is symbolic), its parts (if it has parts), and the classes of objects which it contains or which contain the object set. We will now consider classification, attribution, determination and quantification in more detail.

In the discussion of processes (Fig. 2), a distinction was made between processes which are simple and processes which are relative. A similar distinction can be made between object classes which are simple (nominal), i.e., not defined relative to other object classes, and object classes which are relative, i.e., defined relative to some other object class or classes. Examples of relative classes are kinship classes (e.g., father, cousin, uncle). Relative classes are of two types: transitive (ordered) classes and intransitive (i.e., incompletely or partially ordered) classes. Transitive classes are connected by a relation which is transitive. Thus, Sargent is one of an ordered series of object classes: classes which are ordered according to rank. Intransitive classes, like ordered classes, are defined relative to other classes, but the set of object classes does not form a transitive ordered sequence. For example, John is a cousin of Harry indicates that John and Harry both belong to object classes labeled cousins and that the set of cousins of which John is a member and the set of cousins of which Harry is a member are related (i.e., they contain common elements, John and Harry). However, John and Harry can be cousins and Harry and Bob can be cousins without John and Bob being cousins. Thus, the classes are related but the relation is not transitive. A classificatory relation which connects an object set to a second object set which is a transitive class is called an ordered categorical relation (ORD-CAT, see Fig. 5, branch (2) and the corresponding example); a classificatory relation which connects an object set to a second object set which is intransitive (i.e., not necessarily transitive) is called an intransitive categorical relation (P-CAT, Fig. 5, branch (3)). A classificatory relation which connects an object set to a second object set which is nominal is called a nominal categorical relation

STAT

IVE

REL

ATIO

NS

- :-c

hang

e1

OR

D-C

AT

(2)

INTR

ANSI

TIVE

P-

CAT

(3

)

CAT

(4

)

IDEN

T (5

)

5

POIN

T ix1

0 (6

) [+

dere

rmin

atel

EX

TEN

SIVE

(H

ETR

IC)

-I

RAN

SITI

’JE

--L

c+ex

tens

ive1

CO

NTA

INED

PO

INI

EXIl

(7)

ATTR

IBU

TE

[+di

stan

cel

C-de

term

inar

el

C+o

rder

l IT

RIB

OTI

ON

NO

NMET

RIC

OR

D-A

TT

(8)

C-o

bjec

t] C-

dinc

ance

l C+

attri

bute

l IN

TRAN

SITI

VE

NONH

ETRI

C P-

ATT

(9)

ATTR

IRU

W

C+pr

oxi.it

ylC-d

istan

ce1

NOHI

NAL

ATTR

IBU

TE

I-ord

erlc-

prox

imity

1 C

AT-A

TT

(10)

SYM

COLI

C CO

NTEN

T TH

EME,

(1

1)

l+fh

emel

LOC

ATIV

E L+

loca

tionl

TEM

POR

AL

c+rim

e1

FIG

. 5.

Rel

atio

ns i

dent

ifyin

g ob

ject

s: s

tativ

e re

latio

ns.

Exam

ples

: (1

) A b

ird h

as w

ings

(H

ASP)

. Th

e m

achi

ne h

as g

ears

(H

ASP)

. Th

e pl

ant

has

flow

ers

(HAS

P).

The

book

has

pic

ture

s (H

ASP)

. (2

) Joh

n is

a S

arge

nt (O

RD

-CA

T).

(3) J

ohn

is a

cou

sin

of H

arry

(P

-CAT

). (4

) A c

anar

y is

a

bird

(C

AT).

A sh

ove1

is a

tool

(C

AT).

John

is a

teac

her

(CAT

). (5

) Joh

n is

the

fath

er (

IDEN

T).

John

is th

e te

ache

r (ID

ENT)

. Th

e pr

esen

t w

as th

at d

ress

she

is w

earin

g (ID

ENT)

. (6

) Joh

n is

six

fee

t (D

EG

O) t

all

(EXT

O).

(7) (

a) J

ohn

is ta

ll (E

XTl).

Jo

hn is

med

ium

hei

ght

(EXT

I):

(b)

Can

arie

s ar

e ye

llow

(E

XTI);

an

d (c

) Jo

hn is

bet

wee

n fiv

e an

d si

x fe

et t

all

(EXT

I).

(8) J

ohn

is d

esce

nded

fro

m G

ener

al F

risbe

e (O

RD

-ATT

). (9

) Joh

n is

mar

ried

to A

lice

(P-A

TT).

(10)

The

cat

is

fem

ale

(CAT

-ATT

). Th

e m

an is

Ger

man

(C

AT-A

TT).

(11)

The

boo

k is

abo

ut C

hina

(T

HEM

El).

The

sign

say

s “s

top”

(T

HEM

EI).

The

balle

t is

abo

ut a

bea

utifu

l sw

an (

THEM

EI).


(CAT, Fig. 5, example (4)). Finally, two objects sets which are identical, i.e., which contain the same elements, are connected by an identity relation (IDENT, Fig. 5, example (5)).

Most attributive relations are extensive, that is, they specify a continuous attribute scale on which an object (or members of an object set) have metric values. An attributive relation which specifies that an object (or each member of an object set) has associated with it a value on a metric scale is called an extensive relation (EXT; Fig. 5, examples (6) and (7)). Examples (6) and (7) illustrate further distinctions which can be made among types of extensive relations. These distinctions will be discussed in subsequent sections. The defining properties of an extensive relation are: (1) the attribute is transitive (marked [+order] in Fig. 5), (2) the attribute is metric, that is, a distance can be defined between pairs of attribute values [+distance], and (3) the attribute scale is continuous [+extensive]. As will be seen in subsequent sections, the critical test for a transitive metric attribute is that comparative statements can be made with respect to the attribute. Thus we have John is tall and John is taller than Bob.

GENERIC

F (NO DETERMINER) C-locationl

DEFINITE DEF C+locationl C+definitel

STATIVE RELATIONS C-change1 -4

I- INDEFINITE (TOKEN) TOX C+locationl C-definite]

NULL

r

0

+01NT NUN0

t uNIv!mSAL v

EXISTENTIAL a

FIG. 6a. Determination and quantification. *Terminal branches. #Nonterminal branches: objects so determined and quantified may be (1) further quantified by the application of any quantifier relation, or (2) further determined and quantified by the application of either determiner relation and the number relation. (See examples 5-10.) Examples: (1) airplanes, all airplanes, (2) no airplanes, (3) an airplane, some airplanes, many airplanes, between 3 and 5 airplanes, (4) the airplane, the airplanes, the three airplanes, (5) none of the airplanes (@), (6) each of the airplanes (t/), (7) there is an airplane from among the airplanes (3), (8) three of the airplanes (NUM), (9) an airplane from among the airplanes (TOK, NUM), and (10) the airplane from among the airplanes (DEF, NUM).


Determiner Quantifier

IVERSAL (l)*

ENERIC

-r C-location1

NULL (a*

GENERIC

-I!

INDEFINITE NUMBER (3)# OBJECT SET C+locationl

C-definite

DEFINITE [+locationl C+definitel

NUMBER (4)#

* Terminal branches

c Non-terminal branches: objects so determined and quantified

may be (1) further quantified by the application of any quantifier relation, or (2) further determined and quantified by the application of either determiner relation and the number relation. (see examples S-10)

Examples:

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

airpl.SIlC3, all airplanes

no airplanes

an airplane, some airplanes, many airplanes, between 3 and 5 airplanes

the airplane, the airplanes, the three airplanes

none of the airplanes (d)

each of the airplanes (v)

there is an airplane from among the airplanes (a)

three of the airplanes (NUM)

an airplane from among the airplanes (TOK,NUM)

the airplane from among the airplanes (DEF.NLM)

FIGURE 6b.

Although most attributes are extensive, there do appear to be a few examples of attributive relations which do not satisfy all three defining properties of extensive relations: [ +order], [ +distance], and [fexten- sive]. The first such class of attributes has the defining features [+order] and [-distance]. An example of such an attribute is descended from, as in John is descended from Bob. The attributive relation which assigns such an attribute to an object is labeled ORD-ATT in Fig. 5. The attribute orders objects (people) but does not necessarily allow a distance to be defined between people. Two other classes of attributes which do


not satisfy any of these properties are: intransitive nonmetric attributes and nominal attributes. The corresponding relations are labeled P-ATT (Fig. 5, example (9)) and CAT-ATT (Fig. 5, example (lo)), respectively. Intransitive attributes are similar to intransitive classes: they are relative attributes which are connected by a relation which is not transitive. Nominal attributes, such as nationalities, are not defined relative to any other attributes.

Determiner relations specify whether an object (or object class) has been selected definitely (DEF) or indefinitely (TOK for “token”) from a generic class of objects. In the absence of a determiner, an object set is generic, i.e., it represents a general class of objects. Generic propositions are relational networks which contain generic objects; indefinite propositions contain objects which have been selected indefinitely; definite propositions contain objects which have been selected definitely. Determiner relations, unlike other relations in the system, are unary, i.e., they involve only one concept. A unary relation may be represented in a network of binary relations by defining the relation as a binary relation having a “dummy” (empty) slot (cf. Table 4 below).

Quantifier relations apply only to countable object sets. The quantifier relations which are defined in the system are null ((a), number (NUM), universal (V), and existential (3). A countable object set which is quantified null is empty. A proposition containing an object set quantified null asserts that no objects from the set satisfy the proposition. The number quantifier identifies the number of objects in a countable object set. As in the case of extensive relations, several types of number relations are possible which differ with respect to the precision of the number information. Types of number relations will be discussed in a subsequent section. A proposition containing an object set quantified with a number relation is valid for the specified number of objects. A universally quantified object set contains every instance of a countable object set; a universally quantified proposition contains a universally quantified object set and applies to every object in the set.

The semantic system requires that every countable object set be quantified. The possible combinations of a determiner and quantifier are indicated in Fig. 6b together with examples. Thus, if an object set is generic (i.e., it does not have a determiner), it must be quantified either universally (example (l), all airplanes) or null (example (2), no airplanes). If an object set is not generic, it must be determined either indefinitely or definitely and it must be quantified with a number relation (examples (3) and (4)). Branches (1) and (2) in the diagram in Fig. 6b are terminal branches, i.e., no further quantification is possible. Branches (3) and (4) indicate object sets which can be determined and quantified further by “re-entering” the tree at the left. Examples of object sets which are determined and quantified further are given in Fig. 6b, ex-


amples (5)-(10). Thus, in example (5), ozone of the airplanes, the null quantifier has been applied to an object set which is already definite (DEF) and plural (NUM). The existential quantifier, unlike the other quantifiers, can only be applied to an object set which is already definite or indefinite and plural. Thus, a proposition containing an existential quantifier asserts that there exists one (or more than one) object from a definite or indefinite object set containing more than one element for which the proposition is valid. The number of objects in the set is specified by a number relation (see Fig. 6b, example (7)).

Degree. The “quantification” of object sets which are not countable is accomplished through the degree relation (DEG; see Fig. 7, examples (8) and (9)) and involves the specification of a value for the object on an extensive attributive scale such as amount. The degree relation assigns to an object having an extensive attribute a value (“degree”) on the extensive attribute scale. The degree relation is not restricted to attributive relations; it can assign a degree to any extensive property of an object or action. Further distinctions involving the degree relation will be discussed in a subsequent section.

Relations identifying actions. Just as an object or object set may have associated with it stative relations which identify the object or object set, an action or class of actions which occupies a “slot” in a case system may also have associated with it relations which identify the action or class of actions, distinguishing the action from other classes of actions. An action together with any identifying relations associated with the action will be referred to as the “manner system” associated with the action. A manner system identifies an action or class of actions by means of manner relations. Figure 7 depicts the classification of manner relations. The classification is similar to the classification of stative relations (Fig. 5). Thus, manner relations, like stative relations, are of two kinds: c1ussiJicator-y relations and attributive relations. A classificatory manner relation connects two classes of actions and specifies that one class of actions is a subset of the other class of actions. For example, running is a subset of the class of actions moving, and sprinting is a subset of running. An attributive manner relation specifies that an action or class of actions has associated with it an attribute. Actions can be further identified by means of locative and temporal relations. We will now consider classificatory and attributive manner relations, and then turn our attention to location and time.

In discussing object classes and classificatory relations which connect objects, a distinction was made between nominal object classes and relative object classes. A similar distinction can be made with respect to actions: nominal classes of actions are not defined relative to other actions, while relative classes of actions are defined relative to other actions. Relative classes of actions, like relative classes of objects, can be


TMSITIVE (ORDINAL) C+orderl

INTRANSITIVE C+proxlmityI

-CLASSIFICATION

t

NOMINAL CLASS r.+action1 C-order]

[-proximity]

K4NNEh -- C-state] POINT r MAN-EXTII r+determinate]

EXTBNSIVE r 7 (TRANSITIVE) ATTRIBUIE ~NTAINED MAN-EXTI C+extensfveJ POINT C+orderl C-deterninate]

ORD-Mm (1)

P-Mm (2)

IDENT (4)

U!LATIONS [DENTIFYING UZION.5 OR iTATES

l- ATTRIBLITION C-action1 C+attributel

1 NOMINAL LATTRIBLtTE MAN-Al-l. (7)

C-dFstance1 C-orderlC-proximity1

-L- POINT DEGO (8) [+determinatel

-DEGBEE C+extensivel

CONTAINED DEGl (9) POINT l-determinate]

t

LOCATIYE C+locationl

TEMPORAL C+t imel

FIG. 7. Relations identifying actions or states. Examples: (1) The man fixed the radio by first taking it apart (ORD-MAN), then replacing a resistor (ORD-MAN), and then putting it back together (ORD-MAN). (2) You can fix the radio by taking it apart (P-MAN), then either replacing the circuit board (P-MAN) or replacing a resistor on the circuit board (P-MAN). (3) The man worked with intense concentration (MAN). The man worked, con- centrating intensely (MAN). The man ran with long even strides (MAN). (4) The man fixed the car by replacing the crankshift (IDENT). (5) The dog ran at a speed (MAN-EXTO) of five miles per hour (DEGO). (6) (a) The dog ran swiftly (MAN-EXTl). The man worked hard (MAN-EXTl). (b) The man drove at a reasonable speed (MAN-EXTl). (c) The man drove between 55 and 60 miles per hour (MAN-EXTl). (7) The man turned the screw counterclockwise (MAN-ATT). (8) The man is sixfeet (DECO) tall (EXTO). (9) (a) The man is very (DEGl) tall. (b) The man is average (DEGI) height. (c) The man is between jive and sixfeet (DEGI) tall.


transitive (i.e., ordered) or intransitive. For example, the actionjxing a radio may consist of a set of actions which form a transitive ordered sequence (see example (l), Fig. 7) or a set of actions which are related in the sense that one action has to be performed before another but the actions do not form a transitive ordered sequence (see example (2), Fig. 7). A classificatory manner relation which connects a class of actions to a second class which is transitive is called an ordered manner relation (ORD-MAN; Fig. 7, branch (1)). A classificatory manner relation which connects a class of actions to a second class which is intransitive is called an intransitive manner relation (P-MAN; Fig. 7, branch (2)). A classificatory manner relation which connects a class of actions to a second nominal class is called a nominal manner relation (MAN; Fig. 7, example (3)). If two classes of actions are identical, i.e., the sets contain the same elements, then they are connected by the identity relation (IDENT, see Fig. 7; example (4)).

Attributive manner relations appear to be of only two types: extensive and nominal. An attributive manner relation which is extensive (MAN- EXT) assigns to an action (or to each member of a class of actions) a value on a continuous attribute scale (see Fig. 7, example (6)). Exten- sive manner relations differ with respect to the precision of the information they provide concerning the value on the attribute scale which is assigned to an action. These distinctions will be discussed in a subsequent section. A nominal attributive manner relation (MAN-ATT) assigns a nominal attribute to an action or class of actions, as in The man turned the screw counterclockwise. It appears as if most attributive manner relations are extensive.

Locative and temporal relations. Both objects and actions can be located in space and time. Thus, objects and actions may have associated with them locative and temporal relations which specify locative and temporal information concerning their respective states and events. An object or action together with any locative relations associated with the object or action will be referred to as the “locative system” associated with the object or action; an object or action together with any temporal relations associated with the object or action will be referred to as the “temporal system” associated with the object or action. The relations which may be used to specify a locative or temporal system for an object or action are presented in Fig. 8.

The locative system involves a set of relations which in various ways represent an object or action as a point, path, or region located within a jield having a specified dimensionality. Thus, for example, an object may be represented as a point (zero-dimensional region) on a line (one- dimensional field), as in The car is on the road; as a point in a two- dimensional field, e.g., The dog is in the yard; and as a point in a three- dimensional field, e.g., The dog is in the house. An action can be

POIN

T

F Lo

t 0.

0 (1

)

ON

TAIN

ED P

OIN

T LO

C 0

.j (j-

1,2,

3)

(2)

CO

NTA

INED

PA

TH O

R R

EGIO

N

LOC

i,j

(i,j-1

,2,3

) (3

)

--i

LOC

ATIV

E AN

D

TEH

POR

AL R

ELAT

ION

S

LCLO

SED

PA

TH

CLO

SEk(

LOC

i,j)

(i,k=

l,Z;

j-2,3

) (4

)

OIX

T IE

n0

(5)

c)

rTI~

rIN

STAN

TAN

EOU

S O

NTA

INED

PO

INT

TEH

l (6

)

FIG

. 8.

Loc

ativ

e an

d te

mpo

ral

rela

tions

. Ex

ampl

es:

(1) T

he d

og is

at

hom

e (L

OC

, 0,

O).

The

man

wor

ks a

t ho

me

(LO

C 0

,O).

(2) (

a) T

he c

ar

is o

n th

e ro

ad

(LO

C 0

,l).

(b)

The

dog

is in

the

@id

(L

OC

0,2

). (c

) Th

e do

g is

in t

he h

ouse

(LO

C 0

,3).

(3) (

a) T

he c

ar d

rove

alo

ng f

he r

oad

(LO

C 1

,l).

ib)

The

fenc

e is

in t

heje

ld

(LO

C 1

,2).

(c) T

he je

t le

ft a

trail

in t

he s

ky (

LOC

1,3

). (d

) The

win

e re

gion

is

in F

ranc

e (L

OC

2,2

). (4

) (a

) Th

e fe

nce

is a

roun

d th

e ya

rd.

The

dog

ran

arou

nd t

he y

ard

(CLO

SE

l(LO

C

1,2)

). (b

) Th

e m

an w

rapp

ed

the

band

age

arou

nd

his

arm

(C

LOS

El(L

OC

2,

3)).

(c) T

he p

aper

is a

roun

d th

e pa

ckag

e (C

LOS

E2(

LOC

2,

3)).(

5) T

he m

an b

roke

the

win

dow

at

six

o’cl

ock

(TE

MO

). (6

) (a)

Th

e m

an a

rrive

d ea

rly

(TE

Ml).

(b

) Th

e m

an b

roke

th

e w

indo

w

durin

g th

e m

orni

ng

(TE

MI).

(c

) Th

e m

urde

r w

as c

omm

itted

so

mef

ime

betw

een

two

and

thre

e AM

(T

EM

l).

(7) T

he m

an w

orke

dfro

m

one

to t

hree

PA4

(TE

MO

). (8

) (a)

The

man

wor

ked

ear/y

(T

EM

l).

(b)

The

man

w

orke

dfor

pa

rt of

the

afte

rnoo

n (T

EM

l).

(c) T

he m

an w

orke

dfor

so

me

perio

d (D

UR

l) be

twee

n I

and

5:O

O PM

(TE

Ml).

(9

) The

man

wor

ked

for

thre

e ho

urs

(DU

RO

). (1

0) (a

) The

man

wor

kedf

or

a lo

ng

time

(DU

Rl).

(b

) The

man

wor

kedf

or

a m

oder

ate

leng

th

oftim

e (D

UR

l).

(c) T

he

man

wor

ked@

be

twee

n on

e an

d th

ree

hour

s (D

UR

l).


represented as occurring at a point in a field, e.g., The man broke the cup in the house. It is possible to specify location without reference to dimensionality, i.e., by locating an object or action as a point which is coincident with another point, e.g., The dog is at home. It is also possible for an object or action to be represented not as a point, but rather as a boundedpath (one-dimensional region), or bounded region having two or three dimensions. For example, The car drove along the road is an event which involves movement along a path in which the path is itself located as a bounded segment of a one-dimensional field (the road) which contains the path. Similarly, The jet left a trail in the sky locates the trail as a path in a three-dimensional field.

The different types of locative information which are illustrated by these examples are represented by the first three locative relations which are depicted as branches (l), (2), and (3) in Fig. 8. The notation which is adopted to label these three types of locative relation requires some explanation. The label LOC i,j denotes a locative relation in which a region of dimensionality i is located within afield of dimensionality j. The first branch, point location, is a locative relation which represents an object or action as a point which is coincident with a second point location. The notation LOC 0,O means that the region has zero dimensions and the field within which the region is located also has zero dimensions (see example (l), Fig. 8). The second branch, contained point location, is a locative relation which represents an object or action as a point which is contained within a field having either one, two, or three dimensions. The notation LOC Oj means that the object or action is represented as a zero-dimensional region (point) within a j-dimensional field (see example (2), Fig. 8). The third branch, contained path or region, is a locative relation which represents an object or action as an i- dimensional region within a j-dimensional field (LOC i,j; see example (3), Fig. 8). Finally, there is a fourth type of locative relation which is illustrated by examples such as The fence is around the yard (example (4a), Fig. 8) and The paper is around the package (example (4c), Fig. 8). These examples can be thought of as related to the branch labeled LOC i,j in the following way. In example (4a), an object which could be represented as a one-dimensional region in a two-dimensional field (example (3b)) has been “closed” to form a closed line. This “closing opera- tion” distinguishes (3b) from (4~). Thus, the relation is labeled CLOSE,(LOC 1,2) to indicate that a one-dimensional region has been closed around a 2-dimensional field, and that the fence has been closed in only one dimension. The possibility of closing a region in more than one dimension is illustrated in examples (4b) and (4~). In (4b), a two- dimensional region has been closed in only one dimension; in (4c), it has been closed in two dimensions. Further distinctions among locative relations will be made in a subsequent section.


The temporal system involves a set of relations which specify the absolute time and elapsed time or duration associated with a state or event. Consider tirst absolute time. An event can be represented in the temporal system as instantaneous or durative, while a state would always be represented as durative. An instantaneous temporal relation (TEM) assigns to an event a point in absolute time. For examples, see Fig. 8, examples (5) and (6). Further distinctions among instantaneous temporal relations which are illustrated by these examples will be discussed in a subsequent section. A durative temporal relation assigns to an event or state an interval in absolute time (see examples (7) and (Q Fig. 8). A durative relation (DUR) assigns an interval of elapsed time to a durative event or state (see examples (9) and (lo), Fig. 8). Further distinctions among durative temporal relations and durative relations will be made in subsequent sections.

Logical structure. Any collection of concepts and relations which define a state or event defines a proposition having a truth value. While by convention, a proposition is regarded as having positive truth value, propositions can be negated by applying a negative operator to any relation in the semantic network which delines the proposition. Negative and other truth-value operators will be discussed in detail in a later section. A logical network consists of a set of propositions and a set of labeled binary relations which connect the set of propositions into a logical network. The relations which define a logical network are of three types: logical relations, causal relations, and algebraic relations.

Logical relations are defined in terms of truth tables involving the pairs of propositions which each relation connects. Logical relations include conjunction (&), disjunction (nonexclusive alternation, OR), logical implication (material conditional, IF), material biconditional (IFF), and contrafactual conditional (COND) relations. A set of propositions which are connected by logical relations will be referred to as a logical system. Detailed definitions of logical relations will be given in a later section.

The causal contrafactual conditional relation or causal relation (CAU) is defined as a relation which expresses one variable (the effect) as a function of another variable (the cause). The directionality of the causal relation is given by the asymmetry of the system of functional relations involving the variables (cf. Simon & Rescher, 1966). The causal relation, thus, is fundamentally different from the contrafactual conditional relation. A set of propositions which are connected by causal relations will be referred to as acausal system.

Algebraic relations are relations which connect pairs of propositions which contain identical transitive or intransitive relations. Thus the propositions corresponding to John is tall and Mary is tall can be connected by an algebraic relation since both involve the transitive relation


EXT (extensive attribute). Algebraic relations are of two types: order relations which connect propositions containing transitive relations, and proximity relations which connect propositions containing intransitive relations. Different types of order and proximity relations are defined in terms of their symmetry and reflexivity properties. For example, an equivalence relation (EQUIV) is an order relation which is symmetric and reflexive (e.g., John and Mary are the same height); and the relation ORD is an order relation which is asymmetric and irreflexive (e.g., John is taller than Mary). In the first example, the two connected propositions are John is tall (to an unspecified degree) and Mary is tall (to an unspecified degree); the relations EQUIV and ORD connect the two propositions and place a relative constraint on the degrees of height associated with John and Mary. Thus, EQUIV constrains their heights to have the same degree, and ORD restricts John’s height to have degree greater than Mary’s height. A set of transitive or intransitive propositions which are connected by order or proximity relations will be referred to as a relative system.

All three systems-logical, causal, and relative-make up a logical structure or logical network. A logical network, like a semantic network, has both a content and a structure. The propositional content of a logical network is the set of propositions which occupy slots in the network. The logical structure of a logical network is what is left after all propositions have been removed from the network leaving “empty slots” in their places. All of these topics will be developed in detail in a subsequent section.

SEMANTIC NETWORKS

In the previous section, a semantic network was described as consisting of a set of concepts which occupy slots in a network of labeled binary relations. The set of concepts defines the content of the network and the network of relations (with the concepts removed) defines the structure. Since it is possible to have networks with identical structure and different content, this distinction between content and structure is of more than just theoretical interest. This section will be principally concerned with the structure of semantic networks. In it we will present (by means of a series of tables) precise definitions of the relations identified in the previous section. Each relation in the system will be defined in terms of a concept-relation-concept triple. A definition will consist of (1) restrictions on the classes of concepts which can occupy slots connected by a relation and (2) a definition of the relation. Altogether, the definitions presented in this section define the structure of the semantic networks described in the previous section.

The semantic networks which were described consist of a number of systems which specify different types of semantic information. Case


systems specify causal systems involving actions; state systems identify objects; manner systems identify actions; and locative and temporal systems specify locative and temporal information concerning events or states. In this section, we will develop a network structure for each of these systems. The network structures which will be developed may be regarded as prototype structures into which concepts may be inserted, thus specifying events or states. The specification of states involves the state, locative, and temporal systems; specification of events involves a case system together with the state, manner, locative, and temporal systems.

Case systems. Case systems are of two types: case systems associated with resultive actions and those associated with processes. The structure of case systems for resultive actions is determined by the components of a causal system, e.g., the system must include a cause, a state or process existing prior to an action, an effect or result of the action, a specification of objects affected by the action, etc.; and by the classification of resultive actions, e.g., into cognitive and physical actions. Similarly, the case system for processes is determined by the physical characteristics of a processive system, e.g., a processive system must include the object undergoing the change associated with the process; and by the classification of processes, e.g., into simple or relative, cognitive or physical processes.

Definitions of case relations involving resultive actions are presented in Table 1. Altogether, these relations define a network structure for resultive case systems. The case system so defined has the following structure into which concepts (or embedded network structures) may be inserted, thus defining a network:

(animate object)* 5 (resultive action) OBJI - (inanimate object) DATI - (animate object) 1 * SOURCE_\ [proposition]*

RESULT_, [proposition]* INST - (object)

5 [proposition]

A single asterisk is used to mark slots which are obligatory for every resultive action. The double asterisk indicates that at least one of the two slots is obligatory when the action is physical and that neither is present when the action is not physical. The case system for resultive actions having inanimate agents has the same structure except that AGT is replaced with I-AGT, the I-AGT slot contains a processive object, and the GOAL1 relation is not present.


Specific actions or classes of actions may place further restrictions on the slots in a case system. For example, if a resultive action is a physical action, the SOURCE and RESULT slots would be restricted to contain propositions representing physical states or processes; if the action is cognitive, these slots would be restricted to contain propositions representing a cognitive process (see Table 1, examples (7)-(9)). As an example of how particular classes of actions constrain concepts and propositions occupying slots in the case system (or case frame), consider the resultive action walk. (Concepts will be denoted by their lexical labels.) The case system for walk is:

(cl) - walk DAT’

E (cl) SOURCE ,(c,> LOCO,0 , ( ), RESULT L(c1) LOCO,0 > ( >]

The SOURCE and RESULT slots are restricted to contain locative propositions, the DATl slot is restricted to contain the same animate object (c,) as the AGT slot, and the object of the locative system is restricted to be identical to the object in the AGT and DATl slots. Actions appear to vary in the degree to which they place constraints on slots in their case systems. It should be possible to determine such restricted case systems for many classes of actions.

The direction of the AGT (and I-AGT) relation is given by the causal ordering: cause + effect. The effect produced by the agent consists of an action and the change associated with the action. All other relations in the case system specify the changes associated with the action and thus distinguish the action from other actions in the same class. Thus, all of these relations may be regarded as set relations, i.e., relations which dif- ferentiate sets (in this case sets of actions) into subsets. The direction of these relations is given by this property. Case systems are ordered in other respects. For example, the SOURCE and RESULT propositions are ordered in time. Furthermore, actions such as walk can be analyzed into causal systems composed of more elementary actions. We will return to these topics later in describing causal and relative systems.

Case relations associated with processes are defined in Table 2. Al- together, these relations define a case system associated with a process. The case system so defined has the following structure.

(animate object)* 5 (process) OBJ2 (inanimate object) 1 **

TABL

E 1

CAS

E R

ELAT

ION

S:

RES

ULT

IVE

ACTI

ON

S

Res

trict

ions

No.

” R

elat

ion

Not

atio

n Le

ft sl

ot

Rig

ht s

lot

Def

initi

on

(1)

Agen

t (A

GT)

(2)

Inan

imat

e ag

ent

(I-A

GT)

(3)

Inst

rum

ent

(INST

)

(4)

Anim

ate

af-

fect

ed o

b-

ject

(D

ATl)

(5)

Inan

imat

e af

fect

ed

obje

ct

(OB

JI)

( 1-

t )

( )a

( )

Anim

ate

Res

ultiv

e ob

ject

ac

tion

Proc

essi

ve

Res

ultiv

e ob

ject

ac

tion

Res

ultiv

e ac

tion

Res

ultiv

e ac

tion

Obj

ect

Anim

ate

obje

ct

( )o

BJl

( 1

Res

ultiv

e In

anim

ate

actio

n ob

ject

Imm

edia

te

anim

ate

caus

e of

an

actio

n re

sulti

ng i

n a

chan

ge

Imm

edia

te i

nani

mat

e pr

oces

sive

cau

se

of a

n ac

tion

resu

lting

in

a ch

ange

Imm

edia

te o

bjec

t in

volv

ed

caus

ally

in

a re

sulti

ve

actio

n ca

used

by

an a

gent

Imm

edia

te a

nim

ate

obje

ct a

ffect

ed b

y (u

nder

goin

g ch

ange

as

a re

sult

of)

a re

sulti

ve

actio

n

Imm

edia

te i

nani

mat

e ob

ject

affe

cted

by

(und

ergo

ing

chan

ge a

s a

resu

lt of

) a

resu

ltive

ac

tion

(6)

Prio

r st

ate

or

even

t (S

OU

RC

E)

(7)

Res

ult

(RES

ULT

)

(8)

Res

ult

(cog

nitiv

e ac

tion)

(9)

Res

ult

(phy

sica

l ac

tion

with

sy

mbo

lic

resu

lt)

( )S

[ ]

Res

ultiv

e ac

tion

( )S

[ ]

resu

ltive

ac

tion

( )S

[( )

PAT

-( 1

THEM

E2

- [

]] C

ogni

tive

resu

ltive

ac

tion

( )

RES

ULT

,

[( )

THEM

EI

, [

II Ph

ysic

al

actio

n

Pro

posi

tion

Stat

e or

pro

cess

imm

edia

tely

prio

r to

an

(sta

te o

r ac

tion

resu

lting

in

a ch

ange

in t

he

proc

ess)

pr

oces

s or

sta

te

Pro

posi

tion

(phy

sica

l pr

oces

s or

st

ate)

Phys

ical

sta

te o

r pr

oces

s im

med

iate

ly

resu

lting

fro

m a

phy

sica

l ac

tion

Pro

posi

tion

cont

aini

ng

a co

gniti

ve

proc

es

Cog

nitiv

e pr

oces

s im

med

iate

ly

resu

lting

fro

m a

cog

nitiv

e sc

ion

Stat

ive

prop

ositi

on

cont

aini

ng

a sy

mbo

lic

obje

ct

Sym

bolic

ob

ject

im

med

iate

ly

resu

lting

fro

m a

phy

sica

l ac

tion

(10)

G

oal

( )B

[ ]

Res

ultiv

e P

ropo

sitio

n Im

med

iate

fut

ure

stat

e or

eve

nt to

war

ds

(GO

ALI

) ac

tion

(eve

nt o

r w

hich

a re

sulti

ve a

ctio

n ca

used

by

an

stat

e)

anim

ate

agen

t is

dire

cted

a N

umbe

rs r

efer

to

the

num

bers

and

num

bere

d ex

ampl

es i

n Fi

g. 3

.

TABL

E 2

CAS

E R

ELAT

ION

S: P

RO

CES

SES

No.

”

(1)

(2)

(3)

(4)

(5)

(6)

Rel

atio

n

Res

trict

ions

Not

atio

n Le

ft sl

ot

Rig

ht s

lot

Def

initi

on

Patie

nt (

PAT)

Inan

imat

e pa

tient

(I-

PA

T)

Rel

ated

ani

mat

e ob

ject

(D

AT2)

Rel

ated

ina

nim

ate

obje

ct (

OB

J2)

Goa

l (G

OA

L2)

Sym

bolic

con

tent

(T

HEM

E2)

PAT

( J-

C

1 An

imat

e ob

ject

( )a

( )

Inan

imat

e pr

oces

sive

ob

ject

( I=

( 1

Proc

ess

OBJ

2 (

) -

( )

Proc

ess

( )a

[

] Pr

oces

s

( )W

[ ]

Cog

nitiv

e pr

oces

s

Proc

ess

Phys

ical

pro

cess

Anim

ate

obje

ct

Inan

imat

e ob

ject

Pro

posi

tion

(an

even

t or

sta

te)

Pro

posi

tion

(an

even

t or

sta

te)

Imm

edia

te a

nim

ate

obje

ct u

nder

goin

g a

chan

ge a

ssoc

iate

d w

ith a

cog

nitiv

e or

ph

ysic

al

proc

ess

Imm

edia

te i

nani

mat

e pr

oces

sive

obj

ect

unde

rgoi

ng c

hang

e as

soci

ated

with

a

phys

ical

pr

oces

s

Imm

edia

te

anim

ate

obje

ct r

elat

ed t

o a

rela

tive

proc

ess

Imm

edia

te i

nani

mat

e ob

ject

rel

ated

to

a re

lativ

e pr

oces

s

Imm

edia

te f

utur

e st

ate

or e

vent

tow

ards

w

hich

a p

roce

ss h

avin

g an

ani

mat

e pa

tient

is

dire

cted

Sym

bolic

con

tent

of a

cog

nitiv

e pr

oces

s

n N

umbe

rs r

efer

to

the

num

bers

and

num

bere

d ex

ampl

es i

n Fi

g. 4

.


The single asterisk denotes a slot which is obligatory for every process; the double asterisk indicates that at least one of the relations OBJ2 or DAT2 must be present if the process is relative; the triple asterisk indicates that the relation THEME2 must be present if the process is cognitive. The case system for processes having inanimate patients has the same structure except that the relation PAT is replaced with I-PAT, the I-PAT slot contains a processive object, and the THEME2 and GOAL2 relations are not present. Just as specific resultive actions may have associated with them case systems which incorporate additional restrictions on certain slots in the system, specific processes or classes of processes may place restrictions on the slots in a case system. For example, the case system for burn is:

(fire> * burn

I I

OBJ2 ( ) **

DAT2 ( 1

Here, the processive object is very closely related to the process. Pro- cesses, like resultive actions, vary substantially in the degree to which they restrict slots in their case systems.

The direction of the PAT (and I-PAT) relation is given by the causal ordering: object (cause) + action (effect). The cause-effect relationship between patient and process may be seen by examining processes which may be transformed into resultive actions. For example, in The man walked, the cause of the process is the patient, since, if the process is transformed into a resultive action (e.g., The man walked to the gate), the man becomes the agent of the action. The cause-effect relationship certainly would be preserved under the transformation from process to resultive action. All other relations in the case system may be regarded as set relations: they further specify the nature of relative and cognitive processes.

It is possible to define case systems which contain unfilled slots. Case systems with “open” or unfilled slots allow one to represent events about which one has only partial knowledge. For example, a speaker may know that an event involving a resultive action occurred without knowing the agent of the action. He may express his partial knowledge of the event by means of a passive sentence. Languages have many devices for expressing incomplete semantic structures. Chafe (1970) has identified a number of such examples in his chapter on derivation. Among his examples of derived forms of expression, several are interesting examples of incomplete case systems containing open or uni?.lled slots. The first example, “experiential attribution, ” involves case systems for cognitive processes in which the PATIENT and THEME2 slots are filled but the processive slot is unfilled, e.g., John is sad:

John - ( ) s sad.

TABL

E 3

STAT

IVE

REL

ATIO

NS:

PA

RT-

WH

OLE

, CLA

SSIF

ICAT

ION

, ATT

RIB

UTI

ON

, SY

MBO

LIC

CO

NTE

NT

Res

trict

ions

No.

” R

elat

ion

Not

atio

n Le

ft sl

ot

Rig

ht s

loth

D

efin

ition

(1)

Part-

who

le (

HAS

P)

( )

a (

) Se

t of

obje

cts

Obj

ect

set

Each

mem

ber

of th

e rig

ht

Cla

ssifi

catio

n

(2)

Tran

sitiv

e cl

ass

(OR

D-C

AT)

(3)

Intra

nsiti

ve

clas

s (P

-CAT

)

(4)

Nom

inal

cla

ss

(CAT

)

(5)

Iden

tity

(IDEN

T)

havi

ng-p

arts

()W

( 1

()a(

)

CAT

()

----

-+(

1

Obj

ect

set

Obj

ect

set

Obj

ect

set

Obj

ect

set

Cla

ss o

f obj

ects

whi

ch i

s co

nnec

ted

to a

t lea

st

two

othe

r ob

ject

cla

sses

by

an

orde

r re

latio

n

Obj

ect

clas

s w

hich

is

conn

ecte

d to

at l

east

on

e ot

her

obje

ct c

lass

by

a p

roxi

mity

re

latio

n

Nom

inal

cl

ass

of o

bjec

ts

()-ID

ENT(

) O

bjec

t se

t

obje

ct s

et is

a p

art

of a

m

embe

r of

the

left

obje

ct s

et

The

right

obj

ect

set i

s a

subs

et o

f the

left

obje

ct

set

The

right

obj

ect

set i

s a

subs

et o

f the

left

obje

ct

set

The

right

obj

ect

set i

s a

subs

et o

f the

left

obje

ct

set

The

right

obj

ect

set i

s id

entic

al

to t

he le

ft ob

ject

set

Attr

ibut

ion

(6)

(7) (8)

(9)

Exte

nsiv

e (p

oint

) (E

XTO

)

Exte

nsiv

e (E

XTI)

(con

tain

ed p

oint

) (a

) O

pen

inte

rval

(b)

Labe

led

clos

ed

inte

rval

(c)

Mea

sure

d cl

osed

inte

rval

Tran

sitiv

e no

n-

met

ric a

ttrib

ute

(OR

D-A

I-I)

Intra

nsiti

ve

non-

m

etric

attr

ibut

e (P

-ATT

)

EXTO

D

ECO

(

)-----

-+(

)-(

1 O

bjec

t se

t

()=(

) O

bjec

t se

t

( )a

( )S

( )

Obj

ect

set

( )

EXTl

3

( )

DEG

l ,

[( 1,

(

)I O

bjec

t se

t

( )O

RD

-ATT

( )

Obj

ect

set

( )S

( )

Obj

ect

set

Exte

nsiv

e at

tribu

te

havi

ng a

mea

sure

d de

gree

Labe

led

open

inte

rval

on

an

attr

ibut

e sc

ale

Exte

nsiv

e at

tribu

te

havi

ng a

deg

ree

with

in

a la

bele

d cl

osed

in

terv

al

Exte

nsiv

e at

tribu

te

havi

ng a

deg

ree

with

in

a m

easu

red

inte

rval

A ca

tego

rical

attr

ibut

e w

hich

con

nect

s th

e ob

- je

ct s

et to

at

leas

t tw

o ot

her

obje

ct s

ets

by a

n or

der

rela

tion

A ca

tego

rical

attr

ibut

e w

hich

con

nect

s th

e ob

- je

ct s

et to

at l

east

one

ot

her

obje

ct s

et b

y a

prox

imity

re

latio

n

The

mea

sure

d at

tribu

te i

s a

prop

erty

of

the

m

embe

rs o

f th

e ob

ject

set

The

attri

bute

va

lue

of

each

mem

ber

of t

he

obje

ct s

et is

with

in

the

labe

led

open

inte

rval

on

the

attri

bute

sc

ale

The

attri

bute

va

lue

of

each

mem

ber

of t

he

obje

ct s

et is

with

in

the

labe

led

clos

ed i

nter

val

on th

e at

tribu

te

scal

e

Attri

bute

va

lue

of e

ach

mem

ber

of t

he o

bjec

t se

t is w

ithin

a m

easu

red

inte

rval

on

the

attri

bute

sc

ale

The

attri

bute

is

a pr

oper

ty

of th

e m

embe

rs o

f th

e ob

ject

se

t

The

attri

bute

is

a pr

oper

ty

of th

e m

embe

rs o

f th

e ob

ject

set

TABL

E 3

(Con

tinue

d)

Res

trict

ions

No.

” R

elat

ion

Not

atio

n Le

ft sl

ot

Rig

ht s

loth

D

efin

ition

(10)

N

omin

al a

ttrib

ute

( )r

n(

) O

bjec

t se

t N

omin

al

attri

bute

Th

e no

min

al a

ttrib

ute

is a

(C

AT-A

TT)

prop

erty

of

the

mem

- be

rs o

f th

e ob

ject

set

(11)

Sy

mbo

lic c

onte

nt

( )-

=+L(

)

Sym

bolic

An

obj

ect,

actio

n,

The

sym

bolic

con

tent

of a

(T

HEM

El)

obje

ct

even

t, or

sta

te

sym

bolic

obj

ect

(pro

posi

tion)

a N

umbe

rs r

efer

to

the

num

bers

and

num

bere

d ex

ampl

es i

n Fi

g. 5

. b R

ight

slo

t re

fers

to

the

slot

imm

edia

tely

fo

llow

ing

the

rela

tion

unde

r co

nsid

erat

ion.


In the second example, “resultive attribution,” only the action and OBJI (or DATl) slots in a resultive case system are filled, e.g., The window is broken:

break 3 window.

In sentences such as this one, the action is represented as if it were an attribute of the affected object. Other examples of “resultive attribution” occur in which an attributive form of expression is used to represent the fact that an object can be affected by an action, e.g., This cereal is edible. The final example involves a case system in which the RESULT slot is filled by a proposition and all other slots in the system are unfilled. In such systems, all that is known is that a change of state involving an attribute of an object has occurred. For example, The road widened expresses the following case system:

( > RESULT [road = wide];

widen represents a “derived verb” signifying that a change of state involving the attribute has taken place. In The workmen widened the road, the agent slot has been filled, but the action slot remains unspecified:

workmen -( >= [road s wide].

State systems. Definitions of stative relations are presented in Tables 3 and 4. Table 3 contains definitions of the part-whole relation (l), classificatory relations (2-9, attributive relations (6-lo), and the THEME1 relation (11). Table 4 presents network structures corresponding to the possible combinations of determiners and quantifiers which were identified in Fig. 6(b). Altogether, the relations defined in these two tables may be combined to define a state system associated with an object. Unlike case systems which consist of a single prototype structure containing obligatory slots, state systems are subject to few constraints on the system as a whole. The principal constraint on a state system is that an object must be determined and quantified, i.e., the state system must contain one of the network structures presented in Table 4. Other than that, a state system consists of a network of stative relations selected from Tables 3 and 4 and is subject only to the constraints these relations impose on their slots.

The definitions of extensive attributive relations and number relations require further explanation. In the previous section extensive relations were defined as relations which are: (1) transitive, (2) metric, and (3) continuous. The transitivity property requires that propositions containing extensive relations may be connected by a transitive order relation (e.g., John is taZler than Bob); the metric property implies that a distance can be defined between two metric propositions (e.g., John is two inches taller than Bob); and the continuity property requires that an extensive

TABL

E 4

STAT

IVE

REL

ATIO

NS:

D

ETER

MIN

ATIO

N

AND

Q

UAN

TIFI

CAT

ION

Res

trict

ions

No.

” D

eter

min

er

Qua

ntifi

er

Not

atio

n Le

ft sl

ot

Mid

dle

slot

R

ight

slo

t D

efin

ition

(1)

- U

NIV

ERSA

L (

) &

( )

(W

Gen

eric

D

umm

y sl

ot

- G

ener

ic c

once

pt

coun

tabl

e ob

ject

set

(2)

- N

ULL

(0

) (

I”0

Gen

eric

Em

pty

set,

- N

ull

gene

ric c

once

pt

coun

tabl

e (0

)

i2

obje

ct s

et

m

(3)

IND

EFIN

ITE

NU

MBE

R:

( $5

(

I=(

1 G

ener

ic

Dum

my

slot

An

int

eger

A

num

ber

of o

bjec

ts is

(T

OW

P

oint

co

unta

ble

sele

cted

inde

finite

ly

obje

ct s

et

from

the

obj

ect

set,

the

num

ber

spec

ified

by

a N

UM

re

latio

n

Con

tain

ed

( )T

OK(

)J

=%(

) po

int

Gen

eric

D

umm

y sl

ot

A la

bele

d op

en o

r A

num

ber

of o

bjec

ts is

co

unta

ble

clos

ed in

trval

se

lect

ed in

defin

itely

ob

ject

set

on

the

set

of

from

the

obj

ect

set,

inte

gers

th

e nu

mbe

r sp

ecifi

ed

by a

NU

Mre

latio

n

Con

tain

ed

poin

t (

)TO

K (

) s

[( ),

( )]

Gen

eric

D

umm

y sl

ot

An o

rder

ed p

air

of

A nu

mbe

r of

obj

ects

is

coun

tabl

e in

tege

rs

sele

cted

inde

fmite

ly

obje

ct

set

from

the

obj

ect

set,

the

num

ber

spec

ified

by

a N

UM

re

latio

n

(4)

DEF

INIT

E N

UM

BER

: (

)B(

)3(

) (D

EW

P

oint

Con

tain

ed

poin

t (

)S(

)S(

) G

ener

ic

Dum

my

slot

.4

labe

led

open

or

A nu

mbe

r of

obj

ects

is

coun

tabl

e cl

osed

inte

rval

se

lect

ed d

efin

itely

ob

ject

set

on

the

set o

f fro

m t

he o

bjec

t se

t, in

tege

rs

the

num

ber

spec

ified

by

a N

UM

re

latio

n

Gen

eric

D

umm

y sl

ot

An i

nteg

er

A nu

mbe

r of

obj

ects

is

coun

tabl

e se

lect

ed d

efin

itely

ob

ject

set

fro

m t

he o

bjec

t se

t, th

e nu

mbe

r sp

ecifi

ed

by a

NU

M

rela

tion

Con

tain

ed

poin

t (

)3(

)J=s

R

1, (

)I G

ener

ic

Dum

my

slot

An

ord

ered

pai

r of

A

num

ber

of o

bjec

ts i

s co

unta

ble

inte

gers

se

lect

ed d

efin

itely

ob

ject

set

fro

m t

he o

bjec

t se

t, th

e nu

mbe

r sp

ecifi

ed

by a

NU

M

rela

tion

0 Th

e nu

mbe

rs r

efer

to

the

num

bers

and

num

bere

d ex

ampl

es i

n Fi

g. 6

.

No.

~ R

elat

ion

TABL

E 5

REL

ATIO

NS

IDET

IFYI

NG

AC

TIO

NS

OR

STA

TES:

M

ANN

ER

AND

D

EGR

EE

Res

trict

ions

Not

atio

n Le

ft sl

ot

Rig

ht s

loth

D

efin

ition

Man

ner

clas

sific

atio

n

(1)

Tran

sitiv

e (

F==+

( 1

Cla

ss o

f (o

rdin

al)

clas

s ac

tions

(O

RD

-MA

N)

(2)

Intra

nsiti

ve

clas

s P-

MAN

(

)-(

1 (P

-MA

N)

(3)

Nom

inal

cla

ss

MAN

(

1-c

1 (M

AN)

(4)

Iden

tity

(IDEN

T)

IDEN

T (

1-c

1

Man

ner

attri

butio

n

(5)

Exte

nsiv

e (p

oint

) (

) M

AN-E

XTO

l (

) D

ECO

,(

)

(MAN

-EXT

O)

Cla

ss o

f ac

tions

Cla

ss o

f N

omin

al

clas

s of

ac

tions

ac

tions

Cla

ss o

f ac

tions

C

lass

of

actio

ns

Cla

ss o

f ac

tions

A cl

ass

of a

ctio

ns w

hich

is

con

nect

ed t

o at

le

ast

two

othe

r cl

asse

s of

act

ions

by

mea

ns o

f an

ord

er

rela

tion

A cl

ass

of a

ctio

ns w

hich

is

con

nect

ed t

o at

le

ast

one

othe

r cl

ass

of a

ctio

ns b

y m

eans

of

a pr

oxim

ity

rela

tion

Exte

nsiv

e at

tribu

te

havi

ng a

mea

sure

d de

gree

The

right

cla

ss o

f ac

tions

is

a s

ubse

t of

the

left

clas

s of

act

ions

The

right

cla

ss o

f ac

tions

is

a s

ubse

t of

the

left

clas

s of

act

ions

The

right

cla

ss o

f ac

tions

is

a s

ubse

t of

the

left

clas

s of

act

ions

The

right

cla

ss o

f ac

tions

is

iden

tical

to

the

left

clas

s of

act

ions

The

attri

bute

who

se v

alue

is

spe

cifie

d by

the

de

gree

rel

atio

n is

a

prop

erty

of

the

act

ion

(6)

Exte

nsiv

e (c

onta

ined

poi

nt)

(MAN

-EXT

l)

(a)

Ope

n in

terv

al

(b)

Labe

led

clos

ed

inte

rval

(c)

Clo

sed

inte

rval

w

ith m

easu

red

endp

oint

s

(7)

Nom

inal

attr

ibut

e (M

AN-A

TT)

Deg

ree

(8)

Poi

nt (

DE

GO

)

(9)

Con

tain

ed p

oint

(D

EG 1

)

(a)

Ope

n in

terv

al

(b)

Labe

led

clos

ed

inte

rval

( )M

AN-E

XT1(

)

( )

MAN

-EXT

I ,

( )

s (

)

( )-(

)=

%[(

),(

)]

( )M

AN-A

TT(

1

DEG

O

( 1-

c 1

Cla

ss o

f ac

tions

La

bele

d op

en in

terv

al

on a

n at

tribu

te

scal

e

Cla

ss o

f ac

tions

Ex

tens

ive

attri

bute

ha

ving

a d

egre

e w

ithin

a

labe

led

clos

ed in

terv

al

Cla

ss o

f ac

tions

Ex

tens

ive

attri

bute

ha

ving

a d

egre

e w

ithin

a

mea

sure

d in

terv

al

Cla

ss o

f ac

tions

N

omin

al

(cat

egor

ical

) at

tribu

te

Exte

nsiv

e R

eal n

umbe

r pl

us u

nit

scal

e”

of m

easu

re

Exte

nsiv

e sc

ale

Labe

led

open

inte

rval

on

the

rea

l lin

e

Exte

nsiv

e sc

ale

Labe

led

clos

ed in

terv

al

on t

he r

eal

line

The

attri

bute

va

lue

of th

e cl

ass

of a

ctio

ns i

s w

ithin

a

labe

led

open

in

terv

al

The

attri

bute

va

lue

of th

e cl

ass

of a

ctio

ns i

s w

ithin

a

labe

led

clos

ed

inte

rval

The

attri

bute

va

lue

of th

e cl

ass

of a

ctio

ns i

s w

ithin

a

mea

sure

d cl

osed

inte

rval

The

nom

inal

attr

ibut

e is

a

prop

erty

of

the

actio

n

Mea

sure

d de

gree

on

an

exte

nsiv

e sc

ale

Deg

ree

on th

e ex

tens

ive

scal

e is

with

in

a la

bele

d op

en in

terv

al

Deg

ree

on t

he e

xten

sive

sc

ale

is w

ithin

a

labe

led

clos

ed in

terv

al

TABL

E 5

(Con

tinue

d)

No.

~ R

elat

ion

Not

atio

n

Res

trict

ions

F

Left

slot

R

ight

slo

th

Def

miti

on

? .“r

(c)

Clo

sed

inte

rval

(

) &

[( 1,

( )I

Exte

nsiv

e O

rder

ed p

air

of r

eal

Deg

ree

on th

e ex

tens

ive

with

mea

sure

d sc

ale

num

bers

plu

s un

it of

sc

ale

is w

ithin

a

endp

oint

s m

easu

re

mea

sure

d cl

osed

in

terv

al

a N

umbe

rs r

efer

to

the

num

bers

and

num

bere

d ex

ampl

es i

n Fi

g. 7

. * R

ight

slo

t re

fers

to

the

slot

imm

edia

tely

fo

llow

ing

the

rela

tion

unde

r co

nsid

erat

ion.

c E

ach

of th

e fo

llow

ing

rela

tions

spe

cifie

s an

ext

ensi

ve

scal

e: E

XT,

MAN

-EXT

, TE

M,

DU

R,

LOC

O,

1 (s

ee F

ig.

8).


relation assign a continuous scale to an object such that a value on the scale can be specified in terms of a real number and unit of measure (cf. Table 5, e.g., John is six feet tall):

J&n - tall s 6 feet.

Four network structures involving extensive attributive relations can occur which differ in the precision of the information they provide concerning the value of an object on an extensive attribute scale. The first type of structure (Table 3, example (6)) involves an extensive point relation and assigns a measured value (degree) to an object on a labeled attribute scale (see the example just given). In the other types of structures, the value of the object on the attribute scale is not specified precisely; rather, the object is located as a point within an interval on the metric scale (contained point relations). Thus, in Table 3, example (7a), an object is assigned a point in an open interval on an attribute scale. For example, John is tall:

John % tall

constrains the degree of John’s height to be greater than some reference value or point of orientation on the attribute scale but does not specify an upper bound on this degree. In Table 3, example (7b), e.g., John is medium height,

John - tall % medium,

the attribute value is within a labeled closed interval on the attribute scale, i.e., there is a lower and upper limit to the attribute value corresponding to two points of orientation. Finally, in Table 3, example (7c), e.g., John is between jive and six feet tall, the attribute value is within a closed interval on the attribute scale with measured endpoints:

John % tall % [5 feet, 6 feet].

Notice that in this case the degree slot contains an ordered pair of numbers corresponding to the lower and upper limits of the interval. The principal distinction which is being made in determining different types of extensive relations is between a relation (EXTO) which is deterministic in the sense that there is no uncertainty about the attribute value of an object, and structures containing a relation (EXTl) in which the actual value of an object on an attribute scale is uncertain or unknown.

The distinctions which have been made in classifying attributive relations can be made with respect to other noncase relations. These distinctions are summarized in Fig. 9. Noncase relations may be transitive, intransitive, or nominal; transitive and intransitive relations may be metric or nonmetric; metric relations may be probabilistic (i.e., involve

-TR

ANSI

TIh

C+o

rder

l

NO

N-C

ASE

REL

ATIO

NS

INTR

ANSI

TIVE

C

+pro

xim

ityl

NO

MIN

AL

L N

ON

MET

RIC

(O

RD

INAL

) C

-dis

tanc

e]

r C

ON

TIN

UO

US

c+ex

tens

ive1

-DET

ERM

INIS

TIC

---

---I

(PO

INT)

L+

dete

rmln

atel

D

ISC

RET

E I-e

xten

sive1

O

RD

-CAT

O

IlD-A

TT

OR

D-M

AN

-L

PRO

BABI

LIST

IC

Lot

0,2

(CO

NTA

INED

PO

INT)

La

c 0.

3 I-d

eter

min

ate1

M

ETR

IC

[+df

stan

ceJ

DET

ERM

INIS

TIC

Lo

t 0.

0 (P

OIN

T)

C+d

eter

.inat

el

NO

NM

YETR

I C

P-

CAT

P-

ATT

t-dist

ance

1 P-

HAN

C-o

rder

] C

AT-A

m

I-pro

xim

ity1

MAN

NA

N-Ai

T

EXTI

D

EGl

TEM

I M

AN-E

XTl

DlJ

Rl

LOC

0.1

EXTO

DEG

O

TEM

O M

AN-E

XTD

D

IJR

O LO

C 0

.0

NUM

O

FIG

. 9.

Pro

perti

es o

f no

ncas

e re

latio

ns.


uncertainty) or deterministic; and finally, metric transitive relations may be continuous (extensive) or discrete. Since the only probabilistic intransitive metric relations which occur are continuous, viz. LOC 0,2 and LOC 0,3 (which are intransitive because they involve two and three dimensional spaced, respectively), the continuous-discrete distinction is not made for intransitive relations. All noncase relations are listed after their appropriate branches in Fig. 9. Thus, Fig. 9 indicates which relations have identical algebraic, metric, and statistical properties.

The following network illustrates many of the stative relations defined in Tables 3 and 4. In addition to specifying several state systems, the example includes processive case systems in which slots in the case systems are filled by embedded networks representing state systems. Note that proper names are considered to be definite and singular and thus do not take determiner and quantifier relations.

(birds L ( )) % (canaries % ( >)

EXTL small

-E

EXT’ yellow

HASP ((wings % ( ) Splural) EXTl small)

John PAT have m (canaries 3 ( ) 5 1)

TT;;igaF (5,7 OZ.)

John PAT have % (friend % ( ) NUMO\ 1) s Bill

Bill 5 have =% [(book TOK_, ( ) =+-% 1)

THEMEl (canaries L= ( ))]

The following text can be generated from this network: Canaries are small yellow birds with small wings. John has a canary. His canary is female and weighs between five and seven ounces. John’s friend Bill has a book about canaries.

Whenever an object or action occurs repeatedly in a network, there is an implied identity relation connecting slots containing the same object or action (e.g., John, have, and canaries in the above example). Brackets or parentheses always enclose slots which contain an embedded network structure. Square brackets enclose propositions. The example also illustrates how a network is constructed from a collection of concept- relation-concept triples. The reader should verify that the slot fillers in the above example satisfy the restrictions imposed on them by the structure as defined in Tables l-4.

Manner systems. Manner relations are defined in Table 5. Defined are


cfussijcatory manner relations: (1) ordinal manner classification (ORD- MAN), (2) intransitive manner classification (P-MAN), (3) nominal classification (MAN), and (4) identity (IDENT); and attributive manner relations: (5, 6a-c) extensive manner attribution (MAN-EXT) and (7) nominal manner attribution (MAN-ATT). As can be seen in Fig. 9, the manner relations ORD-MAN and P-MAN have the same properties as the relations ORD-CAT and P-CAT which classify objects; the manner relations MAN and MAN-ATT have the same properties as the relations CAT and CAT-ATT which classify objects and assign nominal attributes to objects (respectively); and extensive manner relation have the same properties as their counterparts which assign extensive attributes to objects. Thus, manner systems have properties similar to state systems associated with objects.

A principal difference between manner systems and state systems is the absence of determiner and quantifier relations for actions. As will be seen in a subsequent section, actions are determined by locating them in space and time by means of locative and temporal systems. “Quantification” of an action can occur in one of two Gays: either by specifying a degree of an extensive attribute associated with an action, or by specifying the frequency of a repeated action, i.e., the number of times the action has taken place. The latter sort of “quantification” will be represented by means of an iterative aspect operator.

The following network contains examples of many of the manner relations defined in Table 5.

[(man 5 ( ) a 1) S run MAN-EXTI quickly DEGI_ very

MAN > sprint -=+( )] MAN

) iwe cxil ,li2°RD

MAN-ATT > counterclockwise CLOSE1

(LOC1.2) (truck 5 ( ) s 1)

The following text can be generated from the network: The man ran very quickly, sprinting at first and then running at an easy lope. He ran counterclockwise around the track.

Note that in this, and other examples which have been given, tense and aspect information is not included in the network. Tense and aspect operators, which represent tense and aspect information, will be introduced in a subsequent section on relative systems. Locative and temporal relations will be defined in the next section and the order relation ORD


(which also occurs in the example) will be discussed in the section on relative systems.

Locative and temporal systems. Table 6 defines a network structure for the locative and temporal systems. Locative relations are of the four types previously described: point location (LOC O,O), contained point location (LOC O,l, LOC 0,2, and LOC 0,3), contained path or region (LOC l,l, LOC 1,3, LOC 2,3, etc.), and closed path or region (CLOSE,(LOC 1,2), etc.). As is illustrated in Fig. 9, the point locative relation has the same properties as the EXTO, MAN-EXTO, and DEGO relations; and the contained point locative relation LOC 0,l in which an object or action is assigned a point on a line (i.e., in a one-dimensional field) has the same properties as the EXTl , MAN-EXTl , and DEGl relations. Three types of LOC 0,l relations are possible (Table 6, (2a-c)) which correspond to the three types of probabilistic attribution (cf. Ta- ble 3, (7a-c)). The three types are: open interval (e.g., The car is on the road) :

(CUY =+ ( ) = 1) Loco,I road,

labeled closed interval (represented in the same manner as open interval, e.g., The car is on the 1.500 block of University Avenue); and measured closed interval or closed interval with labeled endpoints, e.g., The car is between Washington and Baltimore):

(cur s ( > NUMO, 1) LOCO.1 ~ (Washington, Baltimore).

Since transitivity is a property associated with one-dimensional systems, contained point locative relations which assign a point in a two- or three- dimensional space to an object (LOC 0,2 and LOC 0,3) do not have the transitivity property (cf. Fig. 9).

Locative systems frequently occur as parts of relative systems in which locative propositions are connected by algebraic relations into networks representing information about direction, orientation, and relative position. Relative systems containing locative propositions will be developed in the next section.

Temporal systems are defined by two types of time relations: temporal relations (Table 6, (5)-(g)) and durative relations (examples (9) and (10)). In defining temporal relations, a distinction must be made between relations which assign a point in time to an instantaneous action and relations which assign an interval of time to a durative action or state. Temporal relations may also be deterministic, i.e., assign measured times to actions or states (Table 6, (5) and (7)), or probabilistic, i.e., involve uncertainty with respect to the exact time at which an action or state occurred (Table 6, (6) and (8)). As indicated in Fig. 9, the TEMO relation has the same properties as EXTO while TEMl has the same

TABL

E 6

LOC

ATIV

E AN

D

TEM

POR

AL

REL

ATIO

NS

Res

trict

ions

No.

” R

elat

ion

Not

atio

n Le

ft sl

ot

Rig

ht s

lot

Def

initi

on

Loca

tion

(1)

Poi

nt (

LOC

O,O

)

(2)

Con

tain

ed p

oint

(a)

LOC

O,1

(b)

LOC

O,2

(c)

LOC

O,3

(3)

Con

tain

ed p

ath

or r

egio

n

(a)

LOC

I,1

(b)

LOC

I,2

(c)

LOC

1,3

( )X

( )

Obj

ect

or

Labe

led

or m

easu

red

actio

n po

int

( )=

%(

) O

bjec

t or

ac

tion

()a(

) O

bjec

t or

ac

tion

()=f

L()

Obj

ect

or

actio

n

A la

bele

d on

e-

dim

ensi

onal

fie

ld

(line

)

A la

bele

d tw

o-

dim

ensi

onal

fie

ld

Wan

e)

A la

bele

d th

ree-

di

men

sion

al f

ield

()=%

()

Obj

ect

or

actio

n

()S

()

Obj

ect

or

actio

n

()rn

()

Obj

ect

or

actio

n

A la

bele

d on

e-

dim

ensi

onal

fie

ld

(line

)

A la

bele

d tw

o-

dim

ensi

onal

fie

ld

WW

A la

bele

d th

ree-

di

men

sion

al f

ield

An o

bjec

t or

act

ion

is lo

cate

d at

a m

easu

red

or

labe

led

poin

t

An o

bjec

t or

act

ion

is lo

cate

d at

a p

oint

on

a $

labe

led

line

F F An

obj

ect

or a

ctio

n is

loca

ted

at a

poi

nt i

n a

labe

led

two-

dim

ensi

onal

fie

ld

2 g

An o

bjec

t or

act

ion

is lo

cate

d at

a p

oint

in

a E

labe

led

thre

e-di

men

sion

al

field

I2

g

An o

bjec

t or

act

ion

is lo

cate

d as

a o

ne-

dim

ensi

onal

reg

ion

or p

ath

in a

one

-dim

en-

sion

al f

ield

An o

bjec

t or

act

ion

is lo

cate

d as

a o

ne-d

imen

- si

onal

reg

ion

or p

ath

in a

two-

dim

ensi

onal

fie

ld

An o

bjec

t or

act

ion

is lo

cate

d as

a o

ne-d

imen

- si

onal

reg

ion

or p

ath

in a

thre

e-di

men

sion

al

field

(d)

LOC

2,2

()X()

(4)

Clo

sed

path

or

regi

on

(a)

CLO

SE1

(LO

C1,

2)

CLO

SE1

( )

a.O

C1,

2)) (

)

(b)

CLO

SE1

(LO

C2,

3)

(c)

CLO

SE2

(LO

C2,

3)

Tim

e

(5)

Inst

anta

neou

s (p

oint

)

(6)

Inst

anta

neou

s (c

onta

ined

po

int)

(4

Ope

n in

terv

al

(b)

Labe

led

clos

ed

inte

rval

CLO

SE1

CLO

SE2

()=()

( )a

( )

TEM

I (

1-c

1

Obj

ect

or

actio

n A

labe

led

two-

di

men

sion

al f

ield

Obj

ect

or

actio

n A

labe

led

two-

di

men

sion

al f

ield

Obj

ect

or

actio

n A

labe

led

thre

e-

dim

ensi

onal

fie

ld

Obj

ect

or

actio

n A

labe

led

thre

e-

dim

ensi

onal

fie

ld

Inst

anta

neou

s M

easu

red

poin

t in

ac

tion

time

Inst

anta

neou

s A

labe

led

open

tim

e ac

tion

inte

rval

Inst

anta

neou

s A

labe

led

clos

ed ti

me

actio

n in

terv

al

An o

bjec

t or

act

ion

is lo

cate

d as

a tw

o-di

men

- si

onal

reg

ion

in a

two-

dim

ensi

onal

fie

ld

An o

bjec

t or

act

ion

is lo

cate

d as

a c

lose

d on

e-

dim

ensi

onal

reg

ion

(a li

ne o

r pa

th)

whi

ch

cont

ains

a tw

o-di

men

sion

al

labe

led

field

An o

bjec

t or

act

ion

is lo

cate

d as

a c

lose

d tw

o-

dim

ensi

onal

reg

ion

(clo

sed

in o

ne d

imen

sion

) w

hich

con

tain

s a

thre

e-di

men

sion

al

labe

led

field

An o

bjec

t or

act

ion

is lo

cate

d as

a c

lose

d tw

o-

dim

ensi

onal

reg

ion

(clo

sed

in tw

o-di

men

sion

s)

whi

ch c

onta

ins

a th

ree-

dim

ensi

onal

la

bele

d fie

ld

An in

stan

tane

ous

actio

n is

ass

igne

d a

mea

sure

d po

int

in t

ime

An i

nsta

ntan

eous

act

ion

is a

ssig

ned

a po

int

in

time

on a

labe

led

open

int

erva

l

An i

nsta

ntan

eous

act

ion

is a

ssig

ned

a po

int

in

time

on a

labe

led

clos

ed in

terv

al

TABL

E 6

(Con

tinue

d)

No.

” R

elat

ion

(c)

Mea

sure

d cl

osed

in

terv

al

(7)

Dur

ativ

e (in

terv

al)

(8)

Dur

ativ

e (c

onta

ined

in

terv

al)

(a)

Ope

n in

terv

al

(b)

Labe

led

clos

ed

inte

rval

(c)

Mea

sure

d cl

osed

in

terv

al

Res

trict

ions

Not

atio

n Le

ft sl

ot

Rig

ht s

lot

Def

initi

on

2

( )

TEM

l [(

), (

)] In

stan

tane

ous

Ord

ered

pai

r of

tim

e An

ins

tant

aneo

us a

ctio

n is

ass

igne

d a

poin

t in

T1

actio

n m

easu

rem

ents

tim

e on

a m

easu

red

clos

ed i

nter

val

F 2 (

) TE

MO

[(

), (

)] St

ate

or

Ord

ered

pai

r of

tim

e A

stat

e or

dur

ativ

e ac

tion

is a

ssig

ned

a tim

e m

actio

n m

easu

rem

ents

in

terv

al

havi

ng m

easu

red

begi

nnin

g an

d en

d Fi

po

ints

E Ln

( 1-

c )

Stat

e or

ac

tion

( 1-

c 1

Stat

e or

ac

tion

( )

TEM

l [(

), (

)] St

ate

or

actio

n

Labe

led

open

tim

e in

terv

al

Labe

led

clos

ed t

ime

inte

rval

A st

ate

or d

urat

ive

actio

n is

ass

igne

d a

time

inte

r- va

l w

ithin

a

labe

led

open

int

erva

l

A st

ate

or d

urat

ive

actio

n is

ass

igne

d a

time

inte

r- va

l w

ithin

a

labe

led

clos

ed in

terv

al

Ord

ered

pai

r of

tim

e A

stat

e or

dur

ativ

e ac

tion

is a

ssig

ned

a tim

e in

ter-

mea

sure

men

ts

val

with

in

an in

terv

al

havi

ng m

easu

red

begi

nnin

g an

d en

d po

ints

Dur

atio

n

(9)

Poi

nt

(10)

C

onta

ined

poi

nt

(a)

Ope

n in

terv

al

(b)

Labe

led

clos

ed

inte

rval

(c

) M

easu

red

clos

ed

inte

rval

DURO

(

I-----

-*(

1 St

ate

or

actio

n

DURl

(

)-(

1 St

ate

or

actio

n DU

Rl

( )--

----t(

1

Stat

e or

ac

tion

( ) s

[(

), (

)I St

ate

or

actio

n

Mea

sure

d du

ratio

n (e

laps

ed t

ime)

Labe

led

open

inte

rval

A

stat

e or

dur

ativ

e ac

tion

is a

ssig

ned

a du

ratio

n of

ela

psed

tim

e w

ithin

a la

bele

d op

en in

terv

al o

f ela

psed

tim

e

Labe

led

clos

ed i

nter

- A

stat

e or

dur

ativ

e ac

tion

is a

ssig

ned

a du

ratio

n va

l of

ela

psed

tim

e w

ithin

a la

bele

d cl

osed

inte

rval

of e

laps

ed ti

me

Clo

sed

inte

rval

of

el

apse

d tim

e w

ith

mea

sure

d en

d po

ints

A st

ate

or d

urat

ive

actio

n is

ass

igne

d a

dura

tion

with

in

a cl

osed

inte

rval

of

ela

psed

tim

e w

ith

mea

sure

d en

d po

ints

A st

ate

or d

urat

ive

actio

n is

ass

igne

d a

mea

sure

d du

ratio

n

a N

umbe

rs r

efer

to

num

bere

d ex

ampl

es i

n Fi

g. 8

.


properties as EXTl. Three types of TEMl relation occur which are similar in form to the three types of EXTl relation (see Table 6, (6a-6c), @a-c)).

Durative relations specify a duration for a durative action or state: DURO assigns a measured duration to a durative action or state and DURl specifies an uncertain duration as an elapsed time within an interval of elapsed times. Properties of DURO and DURl relations are indicated in Fig. 9.

Temporal systems, like locative systems, frequently occur as parts of relative systems in which propositions containing temporal relations are connected into networks by algebraic relations. Relative systems containing temporal propositions express such information as temporal order, relative duration, and temporal information usually expressed by subor- dinating conjunctions such as while, until, and since. Relative temporal systems will be developed in the next section.

The following example illustrates the use of locative and temporal systems in conjunction with a resultive case system to specify an event involving a resultive action:

(man = ( ) = l),, AGT dash DATI

Cl

SOURCE

RESULT

2

[Cl Lot (door -3. ( ) = l)]

[Cl Lot (gate 5 ( ) s l)]

TEMl (10 AM, ( 1)

LOC 1.1 buth s ( ) NUMO, 1)

DURO 30 seconds

The subscript c1 on the agent slot is used to represent the information in that slot whenever it recurs in the network. An example of a text which can be generated from this network is the following (tense and aspect information are not represented in the network):

The man dashed along the path from the door to the gate at 10 AM. It took him 30 seconds.

LOGI CAL NETWORKS

While the semantic networks which have been defined are capable of representing a reasonably large class of knowledge structures, there re- main several classes of information which they are not capable of representing. First, there is relative information such as that involved in comparatives, expressions of relative time and location, tense, and aspect. In general, relative structures involve relations between propositions containing noncase relations such as attributive, locative, temporal, and durative relations. Second, there is as yet no mechanism for negating


or in other ways operating on the truth-value of propositions; the propositions which have been defined were considered to have positive truth- value. Third, the semantic networks do not represent logical relations such as conjunction, alternation, and implication which are defined in terms of truth tables for pairs of propositions. Finally, in the semantic networks which have been defined, causal systems were restricted to case systems involving objects, states, and events immediately causally connected to an action. More general causal systems need to be considered which contain case systems as components. In this section relations, operators on relations, and networks will be defined which represent these classes of information.

Logical networks were described previously as consisting of sets of propositions connected into networks by relations of three types: logical relations, causal relations, and algebraic relations. Logical networks are composed of three distinct systems: logical systems, causal systems, and relative systems. Each of these systems consists of sets of propositions which are connected into networks by relations of one of the three types: logical, causal, or algebraic. This section will develop network structures for each of these systems beginning with relative systems and then considering logical and causal systems. Truth-value operators will be defined in conjunction with logical systems.

Relative systems. In defining relations in the state, manner, locative, and temporal systems, a major distinction was made between relations which are relative, i.e., relations which identify objects or actions by specifying relative information about the objects or actions and thus directly relating them to other objects or actions, and relations which are nominal, i.e., relations which identify objects or actions by specifying information about the objects or actions which does not directly relate them to other objects or actions. A relative relation was found to be of one of two kinds depending upon whether the relation is transitive or intransitive (i.e., not necessarily transitive; see Fig. 9).

Algebraic relations connect propositions containing transitive or intransitive relations. A relative system consists of a network of algebraic relations and a set of propositions containing transitive or intransitive relations which occupy slots in the network. Algebraic relations are of two kinds: order relations and proximity relations. Order relations connect propositions containing identical transitive relations; proximity relations connect propositions containing identical intransitive relations. Different types of order and proximity relations may be defined in terms of their symmetry, reflexivity, and transitivity properties. Definitions of order and proximity relations are presented in Table 7; a classification of the order and proximity relations defined in Table 7 is presented in Fig. 10. Figure 10 also provides examples of each of the relations defined in Table 7.

Order relations may be illustrated by the following example in which

TABL

E 7

OR

DER

AN

D P

RO

XIM

ITY

REL

ATIO

NS~

Res

trict

ions

No.

* R

elat

ion

Not

atio

n Le

ft sl

ot

Rig

ht s

lot

Def

initi

on

(1)

(2)

(3)

(4)

EQU

IV

-(EQ

UIV

)

OR

D

- (O

RD

)

[ 1 -

[ EQ

UIV

1

r I<

-(EQ

UIV)

l [

1

OR

D

r I-1

1

[ l-

-~~~

) 1

1

A pr

opos

ition

w

hich

co

ntai

ns a

tran

si-

tive

rela

tionc

A pr

opos

ition

w

hich

co

ntai

ns a

tran

si-

tive

rela

tionC

A pr

opos

ition

w

hich

co

ntai

ns a

tran

si-

tive

rela

tion

A pr

opos

ition

w

hich

co

ntai

ns a

tran

si-

tive

rela

tion

A pr

opos

ition

w

hich

co

ntai

ns a

tran

si-

tive

rela

tion

iden

ti-

cal t

o th

at c

on-

tain

ed i

n th

e le

ft pr

opos

ition

A pr

opos

ition

w

hich

co

ntai

ns a

tran

si-

tive

rela

tion

iden

- tic

al t

o th

at c

on-

tain

ed i

n th

e le

ft pr

opos

ition

A pr

opos

ition

w

hich

co

ntai

ns a

tran

si-

tive

rela

tion

iden

- tic

al t

o th

at c

on-

tain

ed i

n th

e le

ft pr

opos

ition

A pr

opos

ition

w

hich

co

ntai

ns a

tran

si-

tical

to

that

con

- ta

ined

in

the

left

prop

ositi

on

A re

latio

n w

hich

is

sym

met

ric,

refle

xive

an

d tra

nsiti

ved

A re

latio

n w

hich

is

sym

met

ric,

irref

lexi

ve

and

?

intra

nsiti

vee

2 g E z

A re

latio

n w

hich

is

asym

met

ric,

irref

lexi

ve

and

trans

itive

’ (g

reat

er t

han

for

met

ric r

elat

ions

)

A re

latio

n w

hich

is

antis

ymm

etric

, re

flexi

ve

and

trans

itive

(le

ss th

an o

r eq

ual t

o fo

r m

etric

re

latio

ns)

(5)

(6)

(7)

(8)

PRO

X

-(PR

OX)

P-O

RD

-(P-O

RD

)

[ 1

PRO

X -[

1

[ I<

- (P

RO

X)

>[

1

r 1 =

r 1

[ 1

-(P-O

RD)

,[ 1

A pr

opos

ition

w

hich

co

ntai

ns a

n in

tran-

si

tive

rela

tion

A pr

opos

ition

w

hich

co

ntai

ns a

n in

tran-

si

tive

rela

tion

A pr

opos

ition

w

hich

co

ntai

ns a

n in

tran-

si

tive

rela

tion

A pr

opos

ition

w

hich

co

ntai

ns a

n in

tran-

si

tive

rela

tion

A pr

opos

ition

w

hich

co

ntai

ns a

n in

tran-

si

tive

rela

tion

whi

ch i

s id

entic

al

to th

at c

onta

ined

in

the

left

prop

ositi

on

A pr

opos

ition

w

hich

co

ntai

ns a

n in

tran-

si

tive

rela

tion

whi

ch i

s id

entic

al

to th

at c

onta

ined

in

the

left

prop

ositi

on

A pr

opos

ition

w

hich

co

ntai

ns a

n in

tran-

si

tive

rela

tion

whi

ch i

s id

entic

al

to th

at c

onta

ined

in

the

left

prop

ositi

on

A pr

opos

ition

w

hich

co

ntai

ns a

n in

tran-

si

tive

rela

tion

whi

ch i

s id

entic

al

to t

hat

cont

aine

d in

the

lef

t pr

opo-

si

tion

A re

latio

n w

hich

is

sym

met

ric,

refle

xive

an

d in

- tra

nsiti

ve

A re

latio

n w

hich

is

sym

met

ric,

irref

lexi

ve

and

intra

nsiti

ve

A re

latio

n w

hich

is

asym

met

ric,

irref

lexi

ve

and

intra

nsiti

ve

A re

latio

n w

hich

is

antis

ymm

etric

, re

flexi

ve

and

intra

nsiti

ve

’ An

ord

er

rela

tion

is a

ny t

rans

itive

re

latio

n w

hich

con

nect

s co

mpa

rabl

e m

etric

or

nonm

etric

(o

rdin

al)

prop

ositi

ons;

a

prox

imity

re

latio

n is

an

y in

trans

itive

re

latio

n w

hich

con

nect

s co

mpa

rabl

e m

etric

or

nonm

etric

re

latio

ns.

* Num

bers

ref

er t

o nu

mbe

rs i

n Fi

g. 1

0.

c Fi

gure

8 id

entif

ies

prop

ertie

s of

non

case

rel

atio

ns.

’ A

rela

tion

R is

tran

sitiv

e if

aRb

and

bRc

impl

y aR

c; R

is sy

mm

etric

if

aRb

impl

ies

bRa;

R is

ref

lexi

ve

if aR

a is

val

id.

e A r

elat

ion

R is

irre

jexi

ve

if aR

a is

not

val

id;

R is

intra

nsiti

ve

if it

is n

ot n

eces

saril

y tra

nsiti

ve.

f A r

elat

ion

R is

asy

mm

etric

if

aRb

impl

ies

not

bRa.

g

A re

latio

n R

is a

ntis

ymm

etric

if

aRb

impl

ies

bRa

if an

d on

ly if

a =

b.

- TR

ANSI

TIVE

OR

DER

r

- TR

ANSI

TNE

- TR

ANSI

TIVE

ALG

EBR

AIC

R

ELAT

ION

S

I R

EFL

ExN

E

- IN

TRAN

SITI

VE

P-

SYM

MET

RIC

EQU

IV

(11

-(EQ

Ulw

12

1 O

RD

PI

-IOR

D]

I41

PRO

X i5

l “r

-(P

ROX)

16

1 2

P-O

RD

17

1 Fi

u m

l -[P

-ORD

) (8

) .-.

E

FIG

. 10

. Ord

er a

nd p

roxi

mity

re

latio

ns.

Exam

ples

: (1

) Joh

n is

the

sam

e he

ight

as

Bill

(EQ

UIV

). (2

) Joh

n an

d Bi

ll ar

e no

t th

e sa

me

heig

ht

(-(E

QU

IV))

. Jo

hn a

nd B

ill ar

e di

ffere

nt h

eigh

ts (

-(E

QU

IV))

. (3

) Joh

n is

talle

r th

an B

ill (O

RD

). Jo

hn is

to t

he l

eft

of B

ill (O

RD

). (4

) Joh

n is

no

t sh

orte

r th

an B

ill (-

(OR

D))

. Jo

hn is

at

leas

t as

tall

as B

ill (-

(OR

D))

. (5

) Joh

n’s

car

is t

he s

ame

as B

ill’s

car

(PR

OX

). Jo

hn is

by

Alic

e (P

RO

X).

John

is

not

mar

ried

to A

lice

(PR

OX

). Jo

hn a

nd A

lice

are

not

cous

ins

(PR

OX)

. (6

) Jo

hn’s

ca

r is

not

th

e sa

me

as B

ill’s

car

(-(P

RO

X))

. Jo

hn is

not

by

Alic

e (-

(PR

OX

)).

John

is m

arrie

d to

Alic

e (-

(PR

OX

)).

John

and

Alic

e ar

e co

usin

s (-

(PR

OX

)).

(7)

John

is

at

Har

ry’s

le

ft C

P-O

RD

). Jo

hn li

kes

cook

ies

mor

e th

an h

e lik

es s

traw

berri

es

(P-O

RD

). (8

) Joh

n lik

es c

ooki

es a

t le

ast

as m

uch

as h

e lik

es s

traw

- be

rries

(-(

P-O

RD

)).


two propositions containing a transitive attribute (height) are connected by the relation EQUIV which is transitive, symmetric, and reflexive (see Fig. 10, example (1)):

[John s height s ( )Ipl

[Bill 3 height s (

EQurv

)I,, II

(The propositions are labeled p1 and p2 for convenience.) Propositions p1 and pz identify John and Bill as each having an unspecified (unknown) degree on an extensive attribute height. The relation EQUIV connects p1 and pz and constrains the unfilled slots in the two propositions in the following manner. (1) The relation EQUIV is transitive: hence, if we have

[Bob 3 height s ( )I,,

and p2 < EQUIV > p3, thenp, +EQU’V ) p3 is valid. (2) The relation is symmetric:

thus p 1 < EQurv > pz and pz c EQ”lV > p1 are both valid; and (3) the relation is re-

flexive: hence p1 +EQ”lv > p1 is valid. Thus, example (1) constrains the unfilled degree slots to be equivalent. The relation -(EQUIV) is defined to be an order relation which is intransitive, symmetric, and irreflexive. The

proposition p1 I pz similarly will be found to constrain John’s height to be unequal to Bill’s height.

The relation ORD is defined as an order relation which is transitive,

asymmetric, and irreflexive. Thus, in the example: p1 ORD\ pz (Fig. 10, ORD example (3)), the relation ORD is transitive: p1 + ORD

p2 - p3 implies

that p1 % p3 is valid; it is asymmetric: p1 % pz and p2 ORD p1 are

not both valid; and it is irreflexive: p1 % p1 is not valid. The proposition

pl s pz by convention will be taken to constrain the unspecified degree of height associated with John to be greater than that assigned to Bill. The relation -(ORD) is transitive, antisymmetric, and reflexive. Thus, in the

example: p1 * pz (Fig. 10, example (4)), if p1 e pz _-O p3is

valid, then p1 I-(ORD) p3 is valid (transitivity); p, ( -@RW p2 and p1 -CORD) >

pz are both valid only if p1 z p2 (antisymmetry), and p1 m p1

is valid (reflexivity). The proposition p1 z pz thus constrains John’s height to be not less than Bill’s height.

In all of the above examples, the propositions connected by order relations contain the extensive attribute height which is one-dimensional and hence transitive. Since intransitivities are produced by systems having


dimensionality greater than one, a convenient example of a proximity relation is adjacency (Fig. 10, example (5): John is by Alice):

[John w ( >I,, PROX [Alice Lot ( )I,, 3

Propositions p1 and pz in this example contain intransitive locative relations which assign unspecified point locations to John and Alice in a two-dimensional field. The relation PROX is intransitive, symmetric, and reflexive and thus constrains the point locations in the unfilled slots in the following way. (1) The relation PROX is intransitive:

hence, if we have a third locative proposition [Bill m ( )],, such that

pz a p3, it is not necessary thatp, a p3 be valid. (2) The relation

PROX is symmetric: thus p1 a pz and pz s p1 are both valid;

and (3) the relation is reflexive: hence p1 a p1 is valid (John is by himself). The relation -(PROX) is defined to be intransitive, symmetric,

and irreflexive. The proposition p1 a pz will be found similarly to constrain John’s and Alice’s locations to be nonadjacent.

An example of the relation P-ORD which is intransitive, asymmetric, and irreflexive is provided by relative systems representing direction. We will consider as examples relative systems from which the following two sentences can be generated: (1) John is to the left offfurry and (2) John is to Hurry’s left. The first example involves a relative system containing a transitive ORD relation; the second involves the intransitive relation P-ORD. The relative system corresponding to example (1) is:

[John D left (Speaker)],,

[Hurry Lot ( )I,, f 10RD

Proposition p1 assigns to John a point location in an open interval (labeled left (Speaker)) on a line (one-dimensional field) where the direction of the line in space is determined by reference to the speaker. Harry is assigned an unspecified point on the same line. By convention a labeled open interval (e.g., left) is taken as the positive direction on an extensive scale unless it is otherwise marked as the negative direction (with a minus sign). The relation ORD constrains John’s location to be on that half of the speaker-defined left-right axis labeled left. That the connecting relation is transitive can be seen by considering the system:

[John -=% left @peaker)l,, zl

ORD [Hurry m left @peal=%,

[Bob Lot ( )I,, LORD


The relation ORD is transitive, that is p1 % p3, since all three people are located on the same line defined by the speaker thus making the system one-dimensional.

Example (2) involves a relative system in which the transitivity property does not hold. Consider the following relative system:

[John % left W=-w%, P-ORD [Hurry % left (Bob)],, 3

[Bob Lot ( )I,, 2 P-oRD

In this system, p1 assigns to John a point location in an open interval (labeled left) on a line where the orientation of the line is determined by reference to Hurry (not to the speaker). Harry is assigned an unspecified point on the same line, and the relation P-ORD constrains John’s location to be on the left half of the left-right line determined by Harry. That the connecting relation P-ORD is intransitive can be seen from the fact that in the example, p2 assigns to Harry a point location in an open interval on a different line determined by reference to Bob. Thus

the entire system involves two dimensions and p1 P-ORD p3 is not necessarily valid. The relation P-ORD may be seen to be asymmetric and ir-

reflexive since: p2 P-ORD p1 is not valid, and p1 P-ORD p1 is not valid. The relative system corresponding to John is not at Harry’s left may be seen to involve the relation -(P-ORD).

Relative systems connecting propositions containing nonmetric relations are illustrated by the following two examples involving the intransitive nonmetric relations P-CAT and P-ATT: (1)

[John P-ATT married],,

[Alice P-ATT married],, 3 -(PRoX)

(Fig. 10, example (6c)), and (2)

[(cousins 5 ( ) s plural)- John],,

[(cousins 5 ( ) 3 plural)% Alice],, 3 -(PROX)

(Fig. 10, example (6d)). In example (l), p1 and pz assign nonmetric attributes to John and Alice. The connecting relation is the intransitive, symmetric, it-reflexive relation -(PROX). Similarly, in example (2) p1 and pz identify John and Alice as members of the relative class of objects: cousins, and the connecting algebraic relation is also intransitive, symmetric, and irreflexive .

Relative systems representing information about relative location are of three principal types: relative position, direction, andspatial orientation (cf. Leech, 1969). One sort of relative position, adjacency, has already


been presented as an example of the relation PROX. Another sort of relative position, relative distance, requires the introduction of an additional algebraic relation, the distance relation.

The distance relation (D), unlike other algebraic relations which have been presented, connects only propositions containing metric relations. The distance relation connects propositions containing relations which are either transitive (one-dimensional) or intransitive (two- or three- dimensional). The distance relation is defined as a symmetric function D(p,, pz) which assigns to a pair of metric propositions a distance having the following three properties: (1) D(p,, p2) 2 0 for every pair of propositions p1 and pz (positivity), (2) D(p,, pl) = 0, and (3) D(p,, pz) + D(p,, p3) 2 D(p,, p3) (the triangle inequality). The distance relation will be represented in network form as follows:

[PI, P21S ( > where p1 and p2 are any pair of metric propositions and the right slot contains a positive real number. A distance, like any other metric value, may be a measured point value (i.e., a determinate measured distance) or it may be specified probabilistically as a point contained in an interval. The interval may be either labeled (open or closed) or have measured endpoints. Suppose two locative propositions are:

[New York D ( )IpI

[Philadelphia B ( )lDz.

The following are examples of each type of distance relation:

[PI, p,]% 100 miles (point valued),

[PI, P21s near (labeled open interval),

Ip,, ~~1% (75 miles, ( )) (open interval with measured endpoint)

[pl, ~~1% moderate (labeled closed interval)

[pl, p$+ (75, 100 miles) (closed interval with measured endpoints)

Sentences which may be generated from these examples are: It is ZOO miles from New York to Philadelphia, New York is near Philadelphia, It is more than 75 miles from New York to Philadelphia, New York and Philadelphia are moderately close, etc.

The distance relation can be used in conjunction with the order relation, ORD, to represent still more complex kinds of relative distance such as underlie the expressions: (1) The house is nearer than the church and (2) The house is near but the church is nearer. Example (1) may be derived from the relative system:


[Speaker = ( j],

[(house = ( j = 1) = ( )lpl

[(church - ( j =ff+ 1) = ( j],,

KPo> PIIS ( )I 3

ORD

[[PO, P21S c >I where p0 denotes a locative proposition specifying the (unknown) location of the speaker or writer. The relation ORD constrains the distance from the speaker to the house to be less than from the speaker to the church. The connecting relation is transitive because distances are transitive. Example (2) may be derived from the relative system:

KPO, PIIS near1 II

ORD

[[PO, P21s near1

Relative systems representing the second type of relative location, direction, have already been presented in illustrating the relation P-ORD. Other directional systems can be considered involving other reference axes (e.g., above-below, back-front, etc.).

The third type of relative location, spatial orientation, involves relative systems which establish an ordering of objects in terms of relative distance from a point of orientation along a line on which all of the objects fall. Consider the example: The farm is beyond the village which may be generated from the following relative system:

[(Speaker) Lot ( j],,

[Cfarm 5 ( j S I)5 ( )I*,

[(village S ( j S 1) Lot ( )Ipz

[[PO, PrlS ( )I ORD

[[PO> P213 ( )I J The principal difference between spatial orientation and relative distance systems is that relative systems for spatial orientation involve l-dimensional locative propositions; relative distance involves 2- or 3-dimensional locative propositions. Other common expressions of spatial orientation are: across, through, and on this side of.

Relative systems also provide a means for representing relative time. Three types of systems for representing relative time may be distinguished: temporal order systems, systems representing relative duration, and “while” systems (cf. Leech, 1969). Temporal order systems occur whenever two propositions, each of which contains a temporal relation, are


connected by an order relation (e.g., ORD, -(ORD), EQUIV). Temporal order systems can occur both for instantaneous and durative propositions. Let pl(t,) represent a proposition p1 containing a simple (instantaneous) time relation where t, refers to the time assigned to the proposition. If p&J is another such proposition, then

P&) = Pm

signifies that p1 occurred before pz (i.e., that t, < t,);

signifies that p1 occurred not later than pz (i.e., that t, I t,); and

P 10 1) f EQurv ’ Pm

signifies that p1 and pz occurred at the same time. Temporal order systems for durative propositons are represented as follows. Let p1(t,o,, tzcl,) represent a durative proposition containing a closed interval of time (tlu), t,,,J, let p&J denote the beginning point, let p&,,,) denote the endpoint, and let p&,,, t.& be a second durative proposition. Then

P&IS = P&23

signifies that p1 ended before pz began, i.e., that tzcl, < tl(%) (etc.). Temporal order systems also may represent measured intervals of time

between events. Such systems require the algebraic relation difference (-) which connects propositions containing identical transitive metric relations. The difference relation is represented [pl, pJ I, ( ) where p1 and pz are an ordered pair of propositions containing identical transitive metric relations and the right slot contains a real number corresponding to the difference between the metric value associated with p1 and that associated

with pz. Suppose pl(tl) e p&J (or alternatively p&J E pz(tlczJ for durative propositions). Then a relative system representing a measured time interval between p1 and pz is [pz, pl] + ( ), e.g., p1 occurredJive minutes before pz.

Temporal order systems may also represent tense and aspect information. Using the notation which has been adopted for simple and durative propositions, Table 8 presents relative systems which define three tense operators: present (PRES), past (PAST), and future (FUT); and nine aspect operators: simple (no operator), continuous (CONT), completive (COMP), inceptive (INCPT), cessive (CESS), iterative (ITER), iterative- completive (ITER-COMP), iterative-inceptive (ITER-INCPT), and iterative-cessive (ITER-CESS). While the tense and aspect operators defined in Table 8 could be represented as relative systems, it is convenient to represent them as operators on relations. The convention is, in the case

TABL

E 8

TEN

SE A

ND

ASP

ECT

OPE

RAT

OR

S

Ope

rato

r Va

lue

Def

initi

on

Exam

ple

Tens

e (T

EM)a

Aspe

ct (

ASPC

T)”

pres

ent

(PR

ES)

past

(PA

ST)

futu

re (

FUT)

sim

ple

cont

inuo

us (

CO

NT)

co

mpl

etiv

e (C

OM

P)

ince

ptiv

e (IN

CPT

)

cess

ive

(CES

S)

itera

tive

(ITER

)

itera

tive-

com

plet

ive

(ITER

-CO

MP)

itera

tive-

ince

ptiv

e (IT

ER-IN

CPT

)

itera

tive-

cess

ive

(ITER

-CES

S)

PO

b EQU

IV

- Pm

es:

PO

- pa

lres,

PO

5 po

ms~

EQU

IV

P(t)

d -

P, O

RD

P

(L,W

P

(tl)

- P,

O

RD

=

P@*)

P

(tl,t*

Y):

P(t2

) -

PO

P(t&

)e:

P&)

(EQ

U’V

, PO

P(tJ

,)‘:

P(Q

<E

QU

IV, P

, O

RD

P&

J +-

o=P

&)

2=

. .

. -

P,&)

=

P,

OR

D

= P”

&J

pm

- PO

P&)

= P,

P”(

tJ

2=%

P,

He

wal

ks

He

wal

ked

He

will

wal

k E

He

wal

ks

E

He

is w

alki

ng

g

He

has

been

wal

king

3 z

He

begi

ns w

alki

ng

Q

He

stop

s w

alki

ng

$

P”(

tJ

He

repe

ated

ly

wal

ks

g

He

has

been

repe

ated

ly w

alki

ng

z

He

begi

ns t

o re

peat

edly

w

alk

z 2 H

e st

ops

repe

ated

ly

wal

king

2 z

a N

otat

ion:

TE

MW

AS

PCT(

R)

,

(val

ue)

, whe

re R

is a

rela

tion;

-w

here

R

is a

rel

atio

n.

(val

ue)

* P,

deno

tes

a pr

opos

ition

co

ntai

ning

an

open

tim

e sl

ot-th

e or

ient

atio

n pr

opos

irion

; its

tim

e sl

ot c

onta

ins

the

poin

t of

orie

ntat

ion

in t

ime.

CP (

pres

j deno

tes

a pr

opos

ition

con

tain

ing

the

time

rela

tion

-pre

sent

.

d Pet

, den

otes

any

pro

posi

tion

cont

aini

ng a

sim

ple

time

rela

tion-

TEM

O

t, ti

e P(t,

,tJ

deno

tes

a du

rativ

e pr

opos

ition

co

ntai

ning

a c

lose

d tim

e in

terv

al

[tl,tJ

; P

(tJ d

enot

es t

he b

egin

ning

poi

nt;

P(tJ

den

otes

the

end

poin

t. w


of resultive actions or processes, to apply tense and aspect operators to the AGT and PAT relations. In the case of stative propositions, tense and aspect operators are applied to the stative relation contained in the proposition. An action or event occurring in a network without a tense operator is considered to be tenseless and hence generic. Thus, actions are “determined” by tense and aspect operators. Examples of tense and aspect operators are:

TEM ASPCT

John * walk (John was walking), CONT

TEM ASPECT

John ++ walk (John begins walking), INCPT

TEM ASPCT

John (PAT) walk (John walked six times). PAST

ITER = 6

Systems representing relative duration consist of durative propositions containing durative relations (DUR) in which the propositions are connected by an order relation. Thus, for example:

TEM

[Alice (PAT) PAST study

TEM ORD

[(Speaker) 9 study =+( )]

may be expressed: Alice studied for a longer time than I. “While” systems involve order relations connecting durative prop-

ositions containing closed temporal intervals where the boundaries of the intervals may be unspecified. “While” systems are of four types, as illustrated by the following sentence examples: (1) co-extensive intervals of time (Alice was at home while Z was at the lecture), (2) point contained within a temporal interval (When I looked away, Billy grabbed the toy), (3) “until” and “since” (John’s ideas have changed since he went to the lecture), and (4) temporal interval contained within an interval of time (John talked to us while we were on vacation). The relative systems for these cases have the following forms:

(1) Co-extensive intervals:

p&J ( EQ”rv > p&,,) (same beginning points)

p&IJ < EQUIV ’ pAb,,J (same endpoints),


(2) Point contained within an interval:

P&o,, t,,,J is a durative proposition, pz(tJ is an instantaneous proposition,

P&,1,) -C’RD) , P2(t2) -(OR@ ~

P&U,)>

(3) “until” and “since”:

(p,(t& ( EQUIV ’ pz(tlcX,) (endpoint of p1 coincides with beginning of p2),

(4) interval contained within an interval (pz contained within pl):

P&J e P&S

P&1,) i -(ORD) P&J

Logical systems. While propositions defined in a semantic network are by convention considered to have positive truth-value, propositions generally can be either true or false. Rather than specify a truth-value for every proposition defined in a network, false propositions are represented by applying a negative operator to a proposition and representing the negated proposition in the network as having positive truth

value. The negative operator is defined for a proposition ( ) % ( ) as

a proposition ( ) % ( ) which is true when ( ) % ( ) is false and

false when ( ) %= ( > is true (Table 10). Since propositions are defined by relational networks, when the negative operator is applied to a relation in a network defining a proposition, it operates on the truth- value of the proposition as a whole.

Definitions of logical relations are presented in Table 9. Logical relations connect pairs of propositions and are defined as in the propositional calculus by means of truth tables for pairs of propositions. A set of propositions occupying slots in a network of logical relations defines a logical system. The following logical relations are defined in Table 9.

Conjunction (&) is defined as a proposition p1 &% pz which is true only if both p1 and pz are true (and is false otherwise). Disjunction (nonex-

clusive alternation) is defined as a proposition p1 +% p2 which is false only when p1 and p2 are both false. Exclusive alternation is defined structurally in terms of the & and OR relations (see Table 9, (3)). The material conditional (IF) is also defined as in the propositional calculus as a

proposition p1 % pz which is false whenever p1 (the antecedent) is true and p2 (the consequent) is false and otherwise is true. The material con-

ditional relation contraposes, that is, both p1 % p2 and -pz % -pl have the same truth table. The material biconditional (IFF) is a proposi-

TABL

E 9

LOG

ICA

L AN

D C

AUSA

L R

ELAT

ION

S

No.

R

elat

ion

Not

atio

n”

Def

initi

on

(1)

Con

junc

tion

(86)

(2)

(3)

Dis

junc

tion

(non

ex-

clus

ive

alte

rnat

ion)

(O

RI

Excl

usiv

e al

tern

atio

n

(4)

Logi

cal

impl

icat

ion

(mat

eria

l co

ndi-

tiona

l) (IF

)

(5)

Mat

eria

l bi

cond

i- tio

nal

(IFF)

(6)

Con

trafa

ctua

l co

nditi

onal

(C

ON

D)

(7)

Cau

sal c

ontra

fact

ual

(CA

U)

[PJ

P21

[PII

A [P

,l

[PII

+=+

[I%1

A pr

opos

ition

w

hich

is

true

only

if b

oth

pi a

nd p

2 are

true

A pr

opos

ition

w

hich

is

true

whe

neve

r p1

is t

rue

or p

z is

tru

e or

bot

h

[PI-P

21

+-s

[PI

-Pzl

A

prop

ositi

on

whi

ch i

s tru

e w

hene

ver

p1 is

tru

e or

p2

is

true

(but

not

bot

h)

[PII

A [P

*l A

prop

ositi

on w

hich

is

fals

e w

hene

ver

p, (t

he a

ntec

eden

t) is

tru

e an

d pz

(th

e co

nseq

uent

) is

fals

e an

d ot

herw

ise

is tr

ue (

cont

rapo

ses:

-pl

+=

-P

z)

[PII

- [P

,l A

prop

ositi

on

whi

ch i

s fa

lse

whe

neve

r p1

is tr

ue a

nd p

2 is

fals

e, a

nd p

, is

fals

e an

d p2

is tr

ue,

and

othe

rwis

e is

true

[PII

= [P

,l A

prop

ositi

on

whi

ch i

s fa

lse

whe

neve

r pi

is tr

ue a

nd p

s is

fals

e, a

nd t

rue

whe

neve

r p1

is t

rue

and

pz is

tru

e; i

ts

truth

val

ue c

anno

t be

det

erm

ined

whe

n p,

is fa

lse

with

- ou

t ref

eren

ce t

o ad

ditio

nal

unst

ated

ant

eced

ent p

ropo

- si

tions

(th

eref

ore

it do

es n

ot n

eces

saril

y co

ntra

pose

)

[PII

-=L

[P,l

A co

ntra

fact

ual

cond

ition

al r

elat

ion

whi

ch e

xpre

sses

one

va

riabl

e (p

2: th

e ef

fect

) as

a fu

nctio

n of

ano

ther

(p,

: th

e ca

use)

; the

asy

mm

etry

of t

he c

ausa

l re

latio

n is

giv

en b

y as

ymm

etry

of t

he s

yste

m o

f fun

ctio

nal

rela

tions

invo

lv-

ing

the

varia

bles

(th

eref

ore

it ne

ver

cont

rapo

ses)

a In

all

case

s, s

lots

con

tain

pro

posi

tions

.


tion p1 +% pz which is false whenever p1 is false and p2 is true, p1 is true and p2 is false, and otherwise is true. The material biconditional is the conjunction of two material conditional propositions.

Material conditional and material biconditional relations occur infre- quently in ordinary discourse. A logical relation which occurs more frequently is the contrujiuctual conditional relation (COND) which is defined,

like the material conditional, as a proposition pl% p2 which is false whenever p1 is true and pz is false, and true whenever p1 is true and pz is true; but, unlike the material conditional, its truth value cannot be determined when p1 is false. For this reason, contrafactual conditional relations do not contrapose. The incompleteness of the truth table for con- t&actual conditional propositions (and the resulting failure of contrafactual conditional propositions to contrapose) is due to the failure to state all of the premises (antecedent propositions) upon which the validity of pz (the consequent) depends (cf. Rescher, 1964).

An example of a contrafactual conditional proposition may be expressed as follows: Zf it rains, Z will open my umbrella, which is generated from the following network:

[(ruin) I-PAT ruin],,

[Speaker % open OBJl (Speaker 5

have OBJ2 (umbrella s ( ) s I))], COND

Pl - 9

The truth table for the contrafactual conditional proposition p1 COND\ q specifies: (1) that the conjunction of p1 and -q is false (i.e., it is false that it ruins and Z do not open my umbrella), and (2) that the conjunction of p1 and q is true (i.e., it rains and Z open my umbrella is true). How-

ever, it does not specify truth values for either -pl A q or -pl G% -4, i.e., it does not specify whether or not I open my umbrella if it doesn’t rain. Suppose we were to accept the additional antecedent proposition:

Zf it is cloudy (pJ, Z will open my umbrella (pz s q). Then the prop-

ositions -pl G% q and -pl A -q are both true. Thus, by accepting

pz COND\ q, a contrafactual conditional proposition was converted into a material conditional. The above example can also be converted into a material biconditional by accepting a different additional antecedent proposition, e.g., Zf it does not ruin, Z will not open my umbrella. In this

case, -pl &% q is false and -pl &% -q is true. The truth table is now that of a material biconditional proposition. These examples demonstrate that there is more than one way in which the unspecified truth values


in a truth table for a contrafactual conditional can be resolved. Contra- factual conditional propositions are thus contextually ambiguous (Rescher, 1964) in the sense that how a contrafactual conditional proposition is resolved depends upon what additional antecedent propositions are chosen to contextualize the proposition.

Thus far propositions have been defined as either true or false. How- ever, speakers often express uncertainty about the validity of a proposition using modal expressions such as may and might to qualify a proposition. A particular qualifier may indicate not only that the truth- value of a proposition is uncertain; it may also indicate how likely the proposition is to be true or false. Just as negation was represented by means of a negative operator which operates on a relation, negating the proposition defined by the relation; other truth-value operators may be defined which indicate that the truth-value of a proposition is uncertain. Two additional truth-value operators are defined in Table 10: (1) a qualifying operator (QUAL) which specifies that a proposition is true with some probability p in the closed interval [O,l]; and (2) an interroga- tive operator (?) which interrogates the truth-value of a proposition. The probability associated with a qualifying operator may be either labeled (e.g., John may go to the store) or measured (e.g., The chances are 1 in 3 that John will go to the store).

There are a number of ways in which “negative information” can be represented in semantic and logical networks. At the conceptual level, an object can be “negatively quantified” by means of the null quantifier @> (e.g., no people); it also can be negatively quantified in a weak manner by means of the NUMl relation and a labeled interval indicating a small number (e.g., few people). At the propositional level, a proposition can be negated by applying the negative operator (-) to a relation in the proposition, or (weakly) by applying the qualifying operator (QUAL). A stative proposition may be implicitly negative if it contains a transitive metric relation which is specified in a “negative” direction (e.g., small, below). Furthermore, other types of negation can be generated by combining different types of negative information in a single proposition (e.g., not many, not above, may not be many).

Causal systems. The causal contrafactual conditional relation (or just causal relation: CAU) is defined in Table 9. The definition indicates first that the causal relation is a kind of contrafactual conditional relation,

i.e., that p1 % pZ has associated with it an incomplete truth table such that if p1 (the cause or causal antecedent) is false, nothing can be said about the validity of pZ (the result or consequent). The causal relation, like the contrafactual conditional relation (COND), does not contrapose. However, a fundamental difference between the contrafactual conditional relation and the causal relation is that the contrafactual conditional can

TABL

E 10

TR

UTH

-VAL

UE

AND

M

OD

AL

OPE

RAT

OR

S

No.

O

pera

tor

Not

atio

n=

Def

initi

on

Trut

h-va

lue

oper

ator

s

(1)

Neg

ativ

e (-)

(2)

Qua

lifie

r (Q

UAL

)

(3)

Inte

rroga

tive

(?)

Mod

al

oper

ator

s

(4)

Nec

essi

ty

(MU

ST)

(5)

Abilit

y (C

AN)

(6)

Qua

lifie

d ne

cess

ity

(QU

AL,

MU

ST)

(7)

Qua

lifie

d ab

ility

(QU

AL,

CAN

)

-(R

I (

)-(

1

( )y

$$h

1

( )L

( )

( )-(

)

Stru

ctur

al

repr

esen

tatio

n

( )a

(

)is

true

whe

n(

) L(

)

is f

alse

and

is fa

lse

whe

n (

) 5

( )

is t

rue;

i.e

.,

( )

5 (

) is

tru

e w

ith

prob

abilit

y 0

( )

-%

( )

is t

rue

with

pr

obab

ility

p (0

<

p <

1);

the

valu

e of

p i

s in

a la

bele

d cl

osed

in

terv

al

The

truth

va

lue

of (

)

5 (

) is

int

erro

gate

d

Ther

e ex

ists

an

uns

tate

d pr

opos

ition

w

hich

im

plie

s or

caus

es

( )

2 (

)

Ther

e ex

ists

an

uns

tate

d pr

opos

ition

w

hich

im

plie

s or

caus

es(

) Q

UAL

(R)

) (

)

[ 1a

c ,A

( )I

!2

[ 1 =

[(

1 -5

( )I

F [G

+K)

), Q

UAU

R)

f (

r l-

CAU

,(

) Q

UAL

(R)+

(

j3

Ther

e ex

ists

w

ith

prob

abilit

y p

(0 <

p

< 1)

an

un-

stat

ed

prop

ositi

on

whi

ch

eith

er

impl

ies

or

caus

es

( )L

( 1

[ I

QU

AL(IF

)

[I Q

lJAL

(CAU

,

Ther

e ex

ists

w

ith

prob

abilit

y p

(0 <

p

< I)

an u

n-

stat

ed

prop

ositi

on

whi

ch

eith

er

impl

ies

or

caus

es

L’ 1

QU

AL(IF

)+,(

) Q

UAL

(R1

( ,,

( )

QU

AL(R

) l

( )

r 1

QU

AL(C

AU)

,[(

1 Q

UAI

- >(

)I

n R

is

any

rela

tion;

(

) 5

( )

is a

pro

posi

tion,

Ex

ampl

es:

(1)

John

di

d na

t go

to

the

stor

e.

Can

arie

s ar

e no

t in

sect

s.

(2)

John

nz

ay g

o to

the

%

stor

e.

John

mig

hr

go t

o th

e st

ore.

(3

) D

id

John

go

to

the

stor

e’?

Are

cana

ries

inse

cts?

(4

) Th

e sa

tellit

e m

ust

retu

rn

to

earth

. Th

e sa

tellit

e ha

s to

\o

retu

rn

to e

arth

. (5

) Jo

hn c

an

lift

the

wei

ght.

(6)

The

sate

llite

may

ha

ve

to r

etur

n to

ear

th.

(7)

John

m

uy

be a

ble

to l

ift

the

wei

ght.


be converted into a material conditional or material biconditional while the causal relation cannot. That is, by specifying additional antecedent propositions, the relation COND can be made to contrapose, but the causal relation cannot be made to contrapose.

The reason for this difference between cause and contrafactual involves another fundamental difference between causal and contrafactual conditional relations, viz. the causal relation, unlike the contrafactual conditional relation, represents an asymmetric functional relation which expresses one variable (p2: the dependent variable, result, or effect) as a function of another variable (PI: the independent variable or cause). The asymmetry of the causal relation is given by the fact that a causal relation is given by the fact that a causal relation does not stand alone but rather represents only one relation in a system of functional relations involving the independent and dependent variables. Causal relations may be conceived of as equations; it is well known that systems of equations can be formulated to represent systems of functional relations such that asymmetric relations occur among individual equations in the system. The reader is referred to a paper by Simon and Rescher (1966) for a detailed discussion of these matters.

To illustrate the defining properties of the causal relation, consider the following example (from Simon et al., 1966): Zf it rains, the wheat will grow or, alternatively, The rain causes the wheat to grow which is derived from the network:

The contrapositive form of this example would be -p2 % -pl (Zf the wheat does not grow, it does not ruin) which is not valid. The causal

proposition p1 % pz may be regarded as a functional relation which expresses the amount of wheat Y as a function of the amount of rain X: Y = f(X). This alone does not explain the asymmetry of the causal relation since the function may possess an inverse, i.e., X = f-‘(Y). However, suppose the amount of rain (PI) and the amount of fertilizer (p3) determine the size of the wheat crop:

Pl -=L pz

p3 CAU

Now, although p1 % pz and p3 % pz are symmetric in the sense that they may be regarded as functional relations which possess inverses, when these relations are embedded in a complete structure (such as that given above), the asymmetry is produced by the asymmetry of the system as a whole.


A causal system is a network of causal relations together with a set of propositions which occupy slots in the network. The case relations AGT and I-AGT are causal relations which are restricted to connecting animate or inanimate processive objects to a resultive action in a case system. Case systems were restricted to representing immediate constituents in a causal system involving a resultive action. Thus, an animate object is an agent of an action if it is a cause of the action and if no other object intervenes causally between the animate object and the action. A case system can often be expanded into a causal system. For example, consider the case system:

TEM

[John 9 break % (window = ( ) = l)],,

(John broke the window). Suppose the system is expanded to include: TEM

[John + r44GsTT) hit OBJl (ball % ( ) - l)],,.

Then the agent relation in p1 is replaced by TEM

P2 -f$+ break.

The system may be expanded still further to include: TEM

[John 3 swing % (bat -% ( ) - I)],,.

Then the agent relation in p2 is replaced by TEM

hit

and the agent relation in p1 is replaced by TEM

pz 9 bryk.

p3 EMU, 1 PAST

What results is a causal system containing case systems as components. The RESULT relation in resultive case systems similarly may be replaced by causal relations as intervening results are introduced into the system.

Causal systems and logical systems, like case systems, may contain unfilled slots. Causal or logical systems with open or unfilled slots allow one to represent logical or causal systems about which one has only partial knowledge. Such systems are often expressed by means of medals


such as must, can, has to, or may have to. Table 10 presents four types of incomplete logical or causal systems which are represented as modal operators on relations: necessity, ability, qualified necessity, and qualified ability. Necessity is represented by the modal operator MUST and is defined as a logical or causal system in which the antecedent proposition or cause is unspecified, e.g., The satellite must return to earth. Ability is represented by the modal operator CAN and is defined as a logical or causal system in which the antecedent proposition or cause is unspecified and the consequent proposition or effect is qualified, e.g., John can lift the weight (viz., There are unstated conditions under which it is possible for John to lift the weight). Qualified necessity is represented by the modal operators QUAL and MUST and is defined as a logical or causal system in which the antecedent proposition or cause is unspecified and the relation connecting the antecedent proposition or cause to the consequent proposition or effect is qualified, e.g., The satellite may have to return to earth. Finally, qualified ability is represented by the modal operators QUAL and CAN and is defined as a logical or causal system in which the antecedent proposition or cause is unspecified, the consequent proposition or effect is qualified, and the relation connecting the antecedent proposition or cause to the consequent proposition or effect is qualified, e.g., John may be able to lift the weight (viz., There may be conditions under which he can lift it).

REPRESENTING ACQUIRED KNOWLEDGE

The relations and operators defined in Tables l-10, the difference and distance relations defined in the last section, and the relative and causal systems together complete the definition of the semantic and logical networks. The networks are well-defined in the sense that all of the relations which occur in the networks are explicitly defined, e.g., in terms of primitive semantic features (cf. section two in which semantic relations were classified on the basis of a small number of semantic “primitives”). Since the definitions of relations include restrictions on the slots which they connect, the model distinguishes well-formed semantic and logical structures from those which are not well-formed. Thus, the system may be regarded as a set of rules for generating well-formed propositional and logical structures. To the extent that particular actions place restrictions on slots in their case systems beyond those already stated in the definition of the case system appropriate for those actions, further conditions for “well-formedness” will have to be specified which are specific to particular actions or classes of actions.

Three interpretations of the semantic and logical networks are possible. The first is simply to regard the networks as abstract data structures. The sole requirement for such an interpretation is that the networks be well-defined. Under this interpretation, one could employ the


network structures defined here as data structures representing informational inputs such as texts or physical events, or as data structures against which subjects’ responses could be analyzed. Neither application requires that the model be correct as a representation of the form of information in human long-term memory.

A second way in which the network structures can be interpreted is as a model of memory structure: a representation of the form in which information structures are coded in long-term memory. As a model of memory structures, a network can be regarded as a model of knowledge structures from which linguistic messages are derived, as a model of the knowledge acquired from particular texts or experienced events, and as a model of world knowledge: the permanent store of knowledge about the world. The present network structures are proposed both as abstract data structures and as a model of the representational format by which information is organized in semantic memory. As a memory model, the emphasis will be placed on semantic and logical networks as models of knowledge structures from which texts are derived and as models of semantic and logical information acquired from texts. The presumption is that much world knowledge is stored in the same representational format.

There is still a third way in which semantic networks may be interpreted, that is, as the semantic or propositional component of a text grammar. In the conception of linguistic productions which has been developing within linguistics, a grammar consists of a propositional base structure and a set of grammatical rules (grammatical transformations) for mapping these propositions directly onto surface sentences. In this view, propositional structures defined without reference to grammatical rules cannot be regarded as a part of a linguistic description of text since the propositional structures represent only the semantic “deep structure” of “surface” sentences or texts. In fact, the sort of propositional structures which may be developed as the semantic component of a text grammar may be substantially different in form from networks which are defined as data structures without reference to language. Furthermore, if a network structure were adopted as a model of memory structure, then it would be subject to the restrictions imposed by psychological data. These data may not lead to the same propositional model as would con- siderations of grammatical constraints. It is possible, however, that as linguistic models are formulated which incorporate the idea of a universal semantic base, they may become very similar to psychological models of memory structure. For these reasons, the network structures presented here are not proposed as components of a linguistic description of text.

The present section will illustrate many aspects of the semantic and logical networks defined in the previous three sections by means of a


network structure which was used to generate a short narrative text-a children’s story entitled About Bill and His Sister. The story is one of four which were written along themes found in children’s textbooks and stories and is intended to be typical of texts used in kindergarten to grade two. The stories were written by Judith 0. Harker for use in her doctoral dissertation at the University of California, Berkeley. In this section we shall also illustrate how network structures may be employed in coding semantic and logical information acquired from texts using data obtained from a sample of Harker’s subjects, kindergarteners who were asked to retell presented stories.

The network structure from which About Bill and His Sister was derived is presented in Fig. 11. The semantic structure can be seen to consist of ten propositions, each of which represents an event, and a set of five stative propositions involving kinship classes. The logical structure consists of a temporal order system in which propositions representing events are connected by order relations into an ordered temporal sequence, and a nonmetric relative system representing kinship relations among participants in the actions. The network contains numerous embedded propositions including embedded relative locative system (viz. a directional system in pZ and an adjacency system in p5). The entire network is connected in two ways: (1) referentially, that is, every time a concept or network structure recurs in the network, there is an implied identity relation connecting slots containing identical concepts or network structures; and (2) by the logical structure, in this case by a set of algebraic relations which connect the propositions into temporal order and non-metric relative systems.

Propositions p1 and pZ each consists of a resultive case system and a temporal order system. In p1 the action move constrains the SOURCE and RESULT slots to contain locative propositions. The SOURCE slot contains an embedded proposition consisting of a processive case system and a locative relation containing an unfilled slot; the RESULT slot also contains a locative proposition have an unfilled slot. Since SOURCE and RESULT slots in a case system are constrained not to contain identical propositions, the unspecified locations are not identical. In p2, the action sit (down) constrains the SOURCE and RESULT slots to contain directional systems which place Bill either above or oy1 the couch (respectively). Also notice that only after couch has been determined and quantified is it able to occupy the object slot for the LOC 0,l relation. Propositions p3 and p4 represent events involving relative processes. The case system in p4 includes in addition a GOAL slot containing a resultive action. Note that no tense operator is specified for an event which is an embedded GOAL.

Proposition p5 contains the resultive action leave, an OBJl slot con-


TM

pl [Bill w rmve DAT1 Bill

F

SoURCE [Bill $$-b roller skate Loc Oy3, ( )I

p2 [Bill

above1 <,

EQUIV

ASPCT

pj [Bill & read

INCPT

(funnies DEF, ( ) Nunl ( ))

1(3)‘t2(3))3

I-+ SOURCE cBill LOC ‘3,3> ( ),

I IRESULT, [Bill 'Oc Os3, (kitchen DEF, () NUMO, 1)

l(4) l ‘2(4))’

FIG. 1 la. Network structure: About Bill and his Sister.

taming an embedded processive proposition identifying the object, and a RESULT slot containing an embedded relative locative system representing adjacency. Proposition ps provides a good example both of a resultive case system in which the contents of the SOURCE and RE- SULT slots are highly constrained by the action and of a network


p5 [Bill NUMO_ 21 =2

[(light DEF, () NUHO, 1) =3

Lot Ot3* (livingroom DEF, () Nun0

TM (I-PAT)

3 PAST ' ( )I

Ccs PAT, use OBJ2, (telephone DEF, ( ) NUHO, 1)I

FIG. 1 lb. Network structure: About Bill and his Sister.

representing incomplete knowledge by means of open slots: the SOURCE slot specifies that the object affected by the action was characterized by an unspecified process and the RESULT slot contains the negated SOURCE proposition. The OBJl slot in ps is an example of how embedded informaion can be built up within a slot.

Proposition p,, like pl, involves a resultive case system containing the action move. Here cs refers to an open slot in the kinship system (Bill’s


pg [cs gg+ tell DAT1 cm

E

RRSuLT cc ) l=% PBI

TEM1 tl 9

[(sons = ( ) % ( )) P-CAT, BIllI 1

[(mother %= ( ) NUMO, l)= I’ -(PROX)

m FOX)

C(dauBhters DEF, ( ) NUM1, ( )) P-CAT, (cJ1 _

[(brothers DEF, ( ) - ( )) P-CAT, Bill1 1 -(PROX)

[(sisters DEF, ( ) NUM1, ( )) P-CAT, (cs)l u

ORD Pl(tl) = p,(t,) = P3(tl(3)) - P4(tl(4))

P4$(4)) = Pg$,) = Pg(t& = P&1 * P&J ,oRD pg(tg) ,oRD Plo(tlo)

FIG. 1 lc. Network structure: About Bill and his Sister.

sister), the RESULT proposition specifies that c, was contained within cq (the living room), the SOURCE location is unspecified, and a GOAL is specified for the action: an embedded processive proposition. Proposi- tion ps is an example of a resultive case system which includes an INST slot; and the RESULT slot contains an embedded processive case system. Proposition p9 is an example of a physical resultive action which has a symbolic result. In this example, the physical result is not specified but its content is specified to be proposition pg. Proposition pl,, is an


example of an incomplete case system in which the action is unspecified, the RESULT proposition is specified (a processive event), and the AGT relation has been replaced by a causal relation connecting the action to P9.

The remainder of the semantic network consists of a set of stative relative propositions involving kinship categories. The relationships among the kinship categories are represented by algebraic relations having the appropriate algebraic properties, viz. intransitivity, symmetry, and ir- reflexivity: -(PROX). Propositions pl-pl,, are connected by means of a set of ORD relations which sequentially order them in time. All ten propositions contain TEM operators, and one, p3, contains the ASPCT operator INCPT (inceptive).

The following story is an example of a text which can be generated from the network in Fig. 11.

One afternoon, Bill came in from roller skating (pJ. He sat down on the couch (p2) and started reading the funnies (p3). Then his mother called him into the kitchen (p4). He left his skates by the couch (p5). Then he turned off the light in the living room @B). His sister came in to use the telephone (p,). Then she slipped and fell on the skates (p&. She told her mother what happened (pg). Bill got in trouble (p,,).

This text represents one realization of the network structure-a realization in which a part of the information in the network is represented in the text. To ascertain precisely what information from the network is represented in the text, the text can be scored against the network by checking each item of information in the network which is explicitly represented in the text in linguistically coded form. An “item” consists of either a concept or a relation. A concept may be represented in a text by the occurrence of a lexical item; a relation may be structurally represented in a text through the application of grammatical rules. To illustrate, compare sentence one of the text to preposition p1 in Fig. 11. The action slot is represented in the text by the verb come, the ACT information by Bill occurring as the subject of an active sentence, the SOURCE relation by the preposition from, the embedded SOURCE proposition by the phrase roller skating occurring within the preposi- tional phrase from roller skating, the RESULT relation and embedded locative proposition by the preposition in occurring immediately after come, and the DAT2 relation and its slot by one afternoon. The embedded locative relation in the SOURCE slot is not represented in the text (but could have been represented as in Bill came in from roller skating outside).

Table 11 lists each item (concept or relation) which occurs in the

REPRESENTING KNOWLEDGE STRUCTURE

TABLE 11 RECALLED ITEMS FROM NETWORK STRUCTURE:

About Bill and his Sister

449

Item

Bill ACT TEM(PAST) move DATl Bill SOURCE

Bill PAT TEM(PAST) rollerskate LOC 0,3”

RESULT Bill LOC 0,3 TEM(PAST)

TEMl afternoon TEMl

-

PI

Proportion recall

.58 -58 .58 S8 .58 .58 .25 .42 .42 .42 .42

0 .42 .42 .33 .42 .17 .I7 .58

Subject*

I 3 4 8 Item

1 1 (1) I Bill 1 1 (1) 1 AGT 1 1 (1) 1 TEM(PAST) 1 1 (1) 1 sit 1 1 (1) 1 DATl 1 1 (1) 1 Bill

(1) SOURCE” (1) Bill”

(1) LOC 0,3”

(1) TEM(PAST)”

(1) RESULT (1) Bill (1) 1 LOC 0,l (1) 1 TEM(PAST) (1) 1 above (1) 1 couch

1 DEF 1 NUMO

1 (1) 1 1 LOC 0,l EQUIV

TEMl

P2 Subject*

Proportion recall 1 3 4 8

.08 1

.08 1

.08 1

.08 1

.08 1

.08 1

.08 1

.08 1

.08 1

.08 1

.08 1

.42 1 1

.42 1 1

.42 1 1

.42 1 1

.08 1

.08 1

.08 1

network, reading from top-left to bottom-right in the network. Items are listed within propositions and relations occurring in the logical structure are also listed. Items which are not explicitly represented in the text are marked with a footnote. The relationship between a network and the semantic and logical information coded in a particular text generated from the network is thus given by simply indicating what items of information in the network are expressed in the text. If subjects are asked to recall the content of a presented text, retell a story, or describe an experienced event, the text which a subject generates can be similarly scored against the network structure from which the text was derived or which represents the informational structure of the experienced event. To illustrate, in Table 11 four subjects’ text recalls have been scored against the network of Fig. 11 in the manner which has been described.

The four subjects were selected from Judith Harker’s sample of 47 kindergarteners at Conejo School in Thousand Oaks, California. The children were tested individually. After being read the story, each child


TABLE 11 (Continued)

p3 P4 Subjectb Subjec@

Proportion Proportion Item recall 1 3 4 8 Item recall 1 3 4 8

Bill .42 1 1 lc, PAT .42 1 1 1 PAT TEM(PAST) .33 1 1 TEM(PAST) ASPCT(INCPT) .08 COMP call read .42 1 1 1 DAT2 OBJ2 .42 1 1 1 Bill

funnies .42 1 1 1 GOAL2 DEF .42 1 1 1 Bill” NUMl .42 1 1 1 AGTa

TEMl .33 1 1 movea DATla BW SOURCE”

Bill” LOC 0,3”

RESULT Bill LOC 0,3

kitchen DEF NUMO 1

TEMl

.58

.58

..58

.58

.58

.58

.33

.08

.08

.08

.08

.08

.17

.33

.42

.42

.42

.42

.42

.58

1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1

1 1

1 1 1 1 1 1 1 1 1 1 1 1 1

was asked to tell the story back to the experimenter. All sessions were tape recorded and each story recall was transcribed. All false starts, hes- itations, and experimenter’s comments were included in the transcript. In some instances, the experimenter found it necessary to probe the child’s memory by providing some information from the text. All such experimenter provided information is indicated for each child in Table 11. Full details concerning the experimental method and analysis of results will be reported in Judith Harker’s doctoral dissertation, “Struc- tural factors affecting acquisition of knowledge from discourse.” Her study includes three age groups (kindergarten, grade 1, and grade 2), a structural manipulation (physical vs. cognitive actions), and a manipulation of the manner in which temporal order is represented in the text. The transcribed recall protocols for the four subjects are as follows.

Subject 1 Cfemale): One afternoon Bill went . . what is it? . _ he stopped reading the funnies. (That’s right) And her mother called him in the kitchen. (Right) And before he


P5

Item Proportion

recall

Bill AGT TEM(PAST) leave OBJl

Bill PAT have OBJ2

skates DEF NUMl plural

SOURCE” cz* LOC 0,2” TEM(PAST)

RESULT

20, 0,2 TEM(PAST) Cl LOC 0.2 PROX

TEMl

.58 58 58 SO .58 .58 .58 .58 .58 .75 .75 .75 .75

.50

.50

.33

.42

.33

.33

.33

.50


Subject*

1 3 4 8 Item

PC

Proportion recall

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1

Bill AGT TEM(PAST) turn OBJl

light DEF NUMO 1

LOC 0,3 livingroom DEF NUMO 1

SOURCE” c3= I-PATa TEM(PAST)”

RESULT C3

I-PAT -

TEM(PAST) TEMl

.33

.33

.33

.33

.33

.33

.33

.25

.25 0

.08

.08

.08

.08 0 0 0 0

.25

.25

.25

.17

.25

.33

Subject*

1 3 4 8

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1

1 1 1 1 1 1

1 1 1 1 1

turned on the light he left his roller skates by the couch. (That’s right) . . . and when the . . is that right? (OK, then his sister did something, what happened to his sister?) She slipped on the roller skates and she told her mother what happened and Bill got in trouble. (That’s right, very good.)

Subject 3 Cfemale): Once this boy named Bill and his sister, when he came back and he we read some funny paper. And then and then he took off his skates, and then his mother called him. And then he took his skates off before he urn turned off the light. And then he took his skates off and turned off the light. And then when his sister was gonna go get the phone, she tripped over the urn skates. (That’s right) and she told the whole story. And Bill got in trouble. (OK)

Subject 4 (female): What’s that first one? (OK, one day Bill came in from roller skating, and what did he do?) He sat down on the couch. (Right) This one is hard. (That’s OK, go to the next one, what happened?) His sister tripped over ‘em, fell on ‘em. (Fell on what?) The



p, P* Pro- Pro- por- Subject* por- Subject0 tion tion

Item recall 1 3 4 8 Item recall 1 3 4 8

CS AGT TEM(PAST) move DATI CS SOURCE” CSQ LOC 0,3” TEM(PASTY RESULT CS LOC 0,3 TEM(PAST)

a :OALl

;AT use OBJ2

telephone DEF NUMO 1

TEMl

.50

.50

.42

.50

.50

.50 0 0 0 0

.25

.25

.25

.17 0

.50

.58

.33

.25

.50

.58

.58

.58

.58

.50

1 1

1 1

AGT get

OBJl 1 1 1 1 1

1 CS .50 (1) 1 1 1 AGT .50 (1) 1 1 1 TEM(PAST) .50 (1) 1 1 1 slip( trip) .58 1 1 1 1 DATl .58 1 1 1 1 CS .58 1 1 1

INST .67 1 1 1 C2 .67 1 1 1 LOC 0,oa 0 ha 0

1 RESULT .33 1 1 CS .50 1 1 1 PAT .25 AGT AGT 1 TEM(PAST) .50 1 1

fall .50 1 1 1 TEMl .50 1 1 1

call 1

1 1

roller skates. (Yeah, how come?) His brother left ‘em there. (That’s right, and then what?) He got in trouble. (And what did his sister do after she fell on them?) I don’t know what she did. (She told somebody about it, right?) She told her mom. (Right) And then he got in trouble.

Subject 8 Cfemale): One early morning Bill urn got up and he got dressed, and then he went into the living room room . . . to read the funnies. (Right) He left his skates on the floor (right) to go into the kitchen. And then his sister comes in and was gonna make a phone call. And she was too tired and she just fell down on the floor and she fell on his skates. (That’s right, and then what did she do?) And then she told her mother urn what happened and Bill got in bad trouble (That’s right, OK.)

In Table 11, each of these protocols has been scored against the network in Fig. 11; an item which is represented within a subject’s protocol is marked with a I; otherwise it is blank. A subject’s protocol is thus represented as a series of dichotomous variables, one for each item



P, P 10 Subject” SubjecF

Proportion Proportion Item recall 13 4 8 Item recall 1 3 4 8

CS AGT TEM(PAST) tell DAT 1 Clll RESULT

THEME1

P8 TEMl

.83 1 1 (1) 1

.83 1 1 (1) 1

.83 1 1 (1) 1

.83 1 1 (1) 1

.83 1 1 1

.83 1 1 1 .42 1 1 (1) 1 .42 1 1 (1) 1 .42 1 1 (1) 1 .75 1 1 (1) 1

Psn 0

CAU” 0

TEM(PAST)” 0

RESULT .83 1 1 1 1 Bill .83 1 1 1 1 PAT .83 1 1 1 1 TEM(PAST) .83 1 1 1 1 be in trouble .83 1 1 1 1 DATza 0

”

T& 0

.83 1 1 1 1

in the network. Items of information provided to the child by the experimenter are marked by l’s enclosed in parentheses. The indented lines in the table indicate groupings of items which are represented as embedded structures occupying slots in the network.

One of the most interesting aspects of these data is the fact that, while subjects do operate on individual items, they tend to recall sets of items as “chunks,” the chunk structure corresponding closely to the embedding structure represented in the network. For example, in proposition p4, subject 1 recalled the embedded locative proposition as a chunk but not the RESULT or GOAL relations connecting the proposition to the action. This example provides evidence that embedded propositions can be processed independently as structural units, that individual relations can be operated on (e.g., deleted), that processive case systems are processed as structural units, and that GOAL information is processed relatively independently of its case system.

These protocols also contain several examples of local operations by subjects on the network. For example, in proposition p3, subject 1 has replaced the inceptive ASPCT operator with the completive, and subjects 3 and 8 have deleted the operator altogether. As another example, in p5, subject 1 has deleted the negative operator the RESULT proposition. Evidence for local operations on a network are important in es- tablishing that the details of the network structure are a valid representation of units of information which can be processed independently.

Examples also occur of subjects generating (“inferring”) information from the network which was not explicitly represented in the input text. Subjects 1, 4, and 8 all generated kinship information which was not explicit in the text, and in p4, subject 8 generated information from the



Temporal order system Kinship system

Subject* Subjectb Proportion Proportion

Relation recall 1 3 4 8 Item recall 1 3 4 8

ORD@l,p2) 0 ORD@z,pd 0 ORD@,,pJ .33 1 1 ORD@~,P~) .17 1 - ORD@,,pd .08 1 ORD@,,p,) .17 ORD@,p,! .25 ORDQJ,,P$ .66 1 1 1 ORD(P,>PJ .75 1 1 1 1

sons” 0 DEF” 0 NUM 1” 0

P-CATa 0 Bill .58

-(PROX) .58 mother 1.00 DEF 1 .oo NUMO 1 .oo 1 1.00

- (PROX)” .42 daughtersa 0 DEFa 0 NUMl” 0

P-CAT” 0 CS” .42

brother9 0 DEFa 0 NUMl” 0

P-CAT” 0 Bill .75

-(PROX) .75 sisters .75 DEF .75 NUMl .75

P-CAT .75

1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

a Item was explicitly coded in the text presented to the subjects. b A 1 indicates that the subject recalled the item; all subjects are selected from the kinder-

garten group.

GOAL slot which was not explicitly represented in the text. Subjects also generate information which is not represented in the network structure at ah. Frederiksen (1975a,b) has argued that the occurrence of such information in text recalls reflects processes fundamental to the comprehension process.

Table 11 also contains proportion recall scores based on analyses of 12 subjects’ recall protocols. The proportion recall scores may be seen to vary considerably according to the location of an item within the network, providing evidence that the network acts as a structural whole affecting the acquisition of its parts. The proportion recall scores also reflect the grouping of items into chunks representing information struc-


tures which are recalled as structural units. While proportion recall scores do not necessarily reflect individual response patterns, for these data when a set of items occurring together are recalled at the same level, the same subjects are recalling each item in the “chunk.” These data exhibit a close correspondence between the embedding structure of the network and the grouping of items in recall. When data are available from a substantial number of subjects, it will be possible to study higher order processing units by analyzing measures of stochastic dependency in the recall of item pairs which directly reflect individual response patterns. The appropriate measures are inter-item tetrachoric correlations, since tetrachoric correlations are not affected by the absolute level of recall of individual items (cf. Frederiksen, 1973).

DISCUSSION

The present research has had two principal objectives. The first was to specify data structures which are sufficiently general that they are capable of representing a variety of information structures from which subjects acquire knowledge-including natural language discourse. The motivation for this first objective was essentially pragmatic: to define a network structure which could be used to represent information structures presented to subjects, principally in the form of written or spoken texts but also as physical events, and to provide a reference structure against which one could code logical and semantic information acquired from a presented text or other information structure. The second objective was to develop an explicit model of the format by which information is represented in semantic memory, a model which is sufficiently general that it is capable of representing semantic information acquired from a very large class of texts. It was found that previous network models were not sufficiently general to be applied at the text level and that therefore they were not satisfactory as models of logical and semantic information which subjects acquire in understanding texts. It appears appropriate in attempting to evaluate the present model, to consider these two objectives separately.

With respect to the hrst objective, the networks which have been presented are extremely general, i.e., they are capable of representing a very large class of semantic and logical structures. They are also well- defined in the sense that was discussed in the previous section, and they are parsimonious since the network structures are “built up” from a small number of semantic primitives (e.g., particularly the development of relative systems). However, the semantic networks are incomplete to the extent that they do not represent case structures for particular actions or classes of actions. As these networks are employed in research on comprehension, it will be important to develop a “dictionary” of actions which specifies those restrictions which particular actions or


classes of actions place on their case systems. A second problem occurs in generating information structures such as texts from semantic and logical networks for presentation to experimental subjects. The generation of event sequences (such as pictures or films) appears to be a relatively straightforward process; however, the generation of texts from semantic and logical networks is at present informal, making use of experimenter’s (and scorers’) informal knowledge of English grammar. While we typically obtain a high degree of agreement among different scorers, it would be desirable to have available a set of procedures for generating texts from network structures, or for generating network structures from texts. It is important to future research on text comprehension to have available such a set of procedures and to implement them in the form of computer programs for generating texts from network structures and for generating networks from texts.

A number of experimental procedures appear to have promise as methods for experimentally verifying network models of memory. If the focus is on memory structures derived from particular informational inputs such as texts rather than on the general store of world knowledge, three techniques suggest themselves. First, one can experimentally manipulate the network structure from which a text (or other informational input) is derived and study effects of such manipulations on recall of items of information from the network structure or on responses to probes derived from the network. Particular network models suggest possible structural manipulations which may or may not affect subjects’ responses. Failure to find effects predicted from structural manipulations would disco&-m those aspects of the model which were used to generate the predictions. Second, one can generate probes from a presented network, and attempt to find a systematic relationship between structural aspects of the network and response latencies to probes. A third method is to estimate probabilities of recall of individual items of information in a network using free recall tasks, and examine correspondences between the location of an item in a network and probability of recall of the item. It is also possible to consider stochastic dependencies in the recall of item pairs by analyzing the joint probabilities of recalling item pairs. As indicated in the previous section, the analysis of interitem dependencies can reveal higher-order informational units or “chunks” which are recalled as structural units. One can investigate correspondences between the embedding structure associated with a network and the chunk structure which may be inferred from stochastic dependencies in the recall of items from the network. The experimental verification of network models of memory will undoubtedly be a lengthy process. A principal justification for the development of detailed models of memory structure is that they make possible systematic experi- mentation and precise assessment of the knowledge which subjects acquire when they understand text.


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(Accepted January 9, 1975)

Documents

Representing logical and semantic structure of knowledge acquired from discourse