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How does the Faculty of Language Relate to Rules,Axioms and Constraints?

Prakash Mondal

Abstract:

This paper explores the link between rules of grammar, grammar formalisms andthe architecture of the language faculty. In doing so, it provides a flexiblemeta-level theory of the language faculty through the postulation of generalaxioms that govern the interaction of different components of grammar. Theidea is simply that such an abstract formulation allows us to view thestructure of the language faculty independently of specific theoreticalframeworks/formalisms. It turns out that the system of rules, axioms andconstraints of grammar cannot be explicitly represented in a general architectureof the language faculty—which circumvents the ontological mismatch of mentalrepresentations and formal/axiomatic properties of language. Rather, thesystem of rules, axioms, constraints of grammar is intentionally projected byhumans, and this projection realizes/instantiates what Dascal (1992) calls‘psychopragmatics’. Relevant implications for linguistic theory, learnabilityand (computational) models of language processing are also explored.

Keywords: Grammar formalisms; language faculty; linguistic theory; meta-level theory; psychopragmatics; representation.

1.IntroductionThe issue of how to characterize the faculty of language with respect torules, principles and axioms of grammar is complex enough. Even if Chomsky(1965, 1980) has over the decades presented the faculty of language as acomputational system with its own domain-specific cognitive structureswhich can be characterized as a system of rules and representations, thenature and form of rules and representations as conceived of within asystem of principles of grammars has been then questioned, reviewed andmodified over the successive phases of development of the theory ofgenerative grammar from the Government and Binding model of generativegrammar to the Minimalist Program (Epstein and Seely 2002, 2006). The pointthat is significant to note but easy to miss in this connection is that allthis discussion has been couched within the system of a specific architectureof the computational system of grammar. Bereft of all such associations,the notion of rules and representations thus construed becomes suspect and

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engenders unclarity regarding the nature and form of rules, principles, andalso the relation between such rules and representations and thearchitecture of the faculty of language (whatever it turns out to be orlook like). Such concerns have been raised by Kac (1987) whose main aim hasbeen to detach the notion of rules from any concerns with how such rulesare represented as cognitive structures in any system or architecture inmind/brain and then construct what he calls principles of etiologicalanalysis relating rules to patterns of ungrammaticality. This is not todeny that such concerns have also appeared elsewhere (Wilks 1972;Langendoen and Postal 1984; Postal 2004; Devitt, 2006; Pullum and Scholz2010).

In fact, the relation between rules and representations and their formwithin a theory-dependent notion of structural descriptions has been a mootpoint and a source of incomprehensibility and confusion (Kuroda 1987;Levelt 2008). And to address this issue with a view to resolving thestalemate, Miller (1999) has proposed the notion of Interpretation Functionthat seeks to characterize the strong generative capacity in theory-independent and formalism-independent terms so that grammar formalisms canbe compared in their strong generative capacity. This suggests that it isthe formalism-dependent or theory-dependent characterization of rules,principles of grammar within the constraints of a particular architecture-specific system that has marred any attempts at understanding rules,constraints and the principles of grammar in the barest possible form inarchitecture-neutral terms. Nowhere has this problem been more evident thanin Kracht (1998) who has argued that grammars characterized by differenttheories can be easily translated back and forth into logics. The same, hehas shown, can be true of transformational generative grammar provided that(the history of) transformation is represented in logics through what hecalls stratification, which keeps a history of transformations. More remarkableis the fact that such translation is aimed at showing the significance oftranslatability of the principles of grammar into axioms of logics whichcan be converted into rules. And such can be achieved, as Kracht argues, atthe expense of snapping off associations with any architecture of grammar.Thus he says:

“The Coding Method is a method that mechanically incorporates any facts aboutlanguage into a rule system. The problematic aspect of it is that it disrespectstotally the architecture of the theories; in other words, it is in itself rathersimple minded. On the other hand, if that is so, it is not clear how the givenarchitecture is justifiable”.

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This is relevant to the issue of how to characterize and much more thanthat, to understand the form of rules, constraints and principles of thefaculty of language in formalism-independent manner. The present papertakes this as the jumping-off point and starts out with this problem. Thecurrent paper aims at sketching out the notion of rules and principles ofgrammar (in a broader sense including syntax, semantics, morphology andphonology) which are formalized in linguistic formalism-independent mannerwithin the bounds of a general architecture of the faculty of language asdeveloped in Mondal (2012). The goals are therefore threefold: (1) tocharacterize the notion of rules and principles of syntax, semantics,morphology and phonology in a more abstract manner independent of anylinguistic formalism; (2) to tie the notion of rules and principles ofsyntax, semantics, morphology and phonology thus formalized to a generalarchitecture of the faculty of language; and (3) to establish a transparenttranslation between the operations of the general architecture of thefaculty of language and the rules and principles of syntax, semantics,morphology and phonology. This paper will mostly be preoccupied with thefirst and second goals and third goal will logically follow on from thefirst two. The general architecture of the faculty of language as developedin Mondal (2012) is general enough to help pave the way for the fulfillmentof the third goal.

With this in the background, let’s move on to present the generalarchitecture of the faculty of language as developed in Mondal (2012),which will help formalize the notion of rules and principles of syntax,semantics, morphology and phonology in a more abstract manner independentof any linguistic formalism thereby fulfilling the first goal. The secondand third goals will fall out of this, leading to possible ramificationsfor linguistic theory, learnability, language processing and therepresentation of the system of axioms, rules and constraints.

2.A general architecture of languageA general functional architecture of language is presented here so that therules and principles of syntax, semantics, morphology and phonology withingrammar can be formalized in the most general fashion. Most of what followscomes from Mondal (2012), who has also shown how such a generalarchitecture of language can be grounded in our cognitive substrate. Oncethe structures and formal principles of the operations in the generalarchitecture of language are understood, this will facilitate the path toan understanding of the issues raised above. We can now approach the

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relevant generalizations. A range of studies in linguistic phenomena(Neelman and Weerman 1998; Hengeveld et al. 2004; Mascaró 2007; Montrul2011; White 2011) have, from different perspectives, suggested that moreinterconnected, fluid interactions among the components of language-syntax, semantics, lexicon, morphology and phonology - can perhaps resolveand handle many theoretical and empirical issues of linguistic phenomena.

Figure 1: A general architecture of language

This is a functional (representational) level elastic architecture of languagein mind/brain (Mondal 2009). The nodes are functional modules, not in aFodorian sense. They are functionally coherent units of representationalresources realized in diffuse, often shared networks of brain regions (Gobet2005; Downing et al. 2005). And the bi-directional arrows representconnections among them. In the proposed architecture above operations can runin any direction involving any number of language domains or components oflanguage like syntax, semantics, morphology etc. for the interpretation of anytype of interaction. Different linguistic phenomena will involve differentsets of interactions among the components. The hallmark of this architectureis its flexibility or elasticity; so the architecture can contract into a one-domaininterfacing configuration or into a two domain or three-domain interfacingconfiguration (and so on), and also expand into a two-domain or three-domainor four-domain interfacing configuration (and so on). Here interface effectsinvolving the components/domains of language can be structurally instantiatedin parallel from and in any direction involving any number of domains or

Lexicon

Syntax Morphology

Semantics

Phonology

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components of language, given that only some content of each as required byothers is available to the others. This is ensured by a number of constraintsoperating over the architecture. The constraints also make sure that thearchitecture does not grow too powerful in being able to run operations in anydirection involving any number of components of language. In fact, it is theseconstraints that give the architecture its elasticity. They are like pressuresthat warp the geometry of the architecture. It may well be argued that theyare actually epigenetically encoded in our language faculty in a form ofcloser but complex coupling between genes, and external as well as internalenvironments (Fitch 2009). The nature and form of these constraints has beenexplicated in details in the subsection below. However, the followingstipulation encapsulates the form of operations in the architecture above.This can be stated as:

Stipulation: For any linguistic phenomenon χ in any language L there must be an interactionI(χ) such that there is a set Ω of linguistic components/domains Lc (Lc =lexicon, syntax, semantics, phonology, morphology, semantics and Ω ⊆ Lc)which are in parallel interaction with each other with τ(I(χ)) where τ is astructural mapping condition, iff I(χ) satisfies a set Ф of constraints thatoperate on I(χ) and | Ω |= Θ and Θ≥ 1.

This stipulation ensures three significant things: (i) any linguisticphenomenon in a language involves an interaction between a numbercomponents/domains of language; (ii) the number of components/domains oflanguage involved in any such interaction must be greater than or equivalentto 1; (iii) any interaction in a linguistic phenomenon must be governed by astructural mapping condition, and an interaction governed by a structural mappingcondition must then be compatible with a set of constraints that operate onpossible forms and ways of interaction among the linguisticcomponents/domains. Thus every interaction is constrained and doublyrestricted, and the constraints emanate from the notion of structural mappingcondition (τ) (explicated below) and more specifically, from a set ofconstraints Ф (to be specified in section 2.1). This will be clearer as weproceed to section 3.

Besides this, it appears to be necessary to clarify a certain number ofconcepts used. A linguistic phenomenon is any phenomenon that involves a kind ofinteraction between any number of components of language for the observedregularities/irregularities found across languages. This is ensured by Θ≥1

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because any linguistic phenomenon may involve either just one linguisticcomponent/domain or more than one. An interaction between any number of componentsof language involves a sort of interfacing between them such that suchinterfacing causes the components of language involved in the interaction tomap required information onto each other, for example, the linguisticphenomenon of split intransitivity- a distinction between ergativity/unaccusativity-causes syntax, lexicon, morphology and semantics to work in tandem and haveimpacts on one another. The notion of interaction will be formalized in Axiom3 in section 3. Structural mapping condition (τ) requires the mapping of as muchlinguistic information at the interfaces between the components/domains oflanguage as is feasible and needed in a given linguistic phenomenon. Thus, forexample, a sentence like ‘John loves the dog he has brought’ will involve anoverlapping range of linguistic phenomena. So for the sentence underconsideration, there will be an involvement of the phenomenon of agreement (toaccount for the agreement between ‘John’ and ‘loves’), the relation of tenseand aspect (the sentence is in present tense and the aspect of the event isdurative), the phenomenon of relativization (it tells us that ‘John loves thedog’ and ‘he has brought’ are two different clauses linked via the internalargument of ‘brought’ by means of a null relative pronoun), the phenomenon ofdisplacement (the internal argument of ‘brought’ does not appear where it isinterpreted), the semantic composition of the parts of the sentence (involvingthe meaning of ‘the dog’ that is restricted by the relative clause ‘he hasbrought’ and the anaphoric link between ‘John’ and ‘he’), the phenomenon ofmapping major (prosodic) phrases and intonational phrases to relevantsyntactic structures (‘John’ may be a different major (prosodic) phrase fromthat contained in ‘loves the dog’ and the relative clause may well be adifferent intonational phrase) and so on. All these phenomena may or may notintersect with each other; but what Structural mapping condition dictates is thateach such phenomenon must be constituted only by the amount of linguisticinformation that the relevant mapping between the components/domains oflanguage involved in the phenomenon requires.

Let’s take, for instance, the phenomenon of mapping major (prosodic) phrasesand intonational phrases to relevant syntactic structures. This phenomenon willonly require relevant information from phonology, syntax and perhapssemantics; the rest is not necessary and adequate only in this sense. Thuseach phenomenon out of an ensemble in any single sentence may involve adifferent interfacing condition on the components/domains of language. To putit in different words, the construction of any sentence in a language ensuesfrom a coalescence of an ensemble of interfacing conditions of the general

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architecture of language. And this is possible because the architecture of thelanguage faculty is elastic; hence Structural mapping condition is an outcome of theelasticity of the general architecture of language in Figure 1. Adequacy ofinformation is the amount of linguistic information as demanded in therequirements of structural mapping condition, so for example, in the linguisticphenomenon of middle constructions (as in ‘These vegetables cut easily’)information about word order/linearity and agreement from syntax (the externalargument ‘these vegetables’ agrees with the verb ‘cut’), the specification ofthe theta-roles of a predicate from lexicon (‘cut’ needs an agent argument anda theme argument, which is a subject here) and the semantic content fromsemantics (the timelessness of the aspectual configuration of the event and anoverall semantic contribution of other parts to the semantic content of thesentence) are to be characterized as adequate information. Any otherinformation from morphology or phonology is not adequate, albeit useful in thetrivial sense of the fulfillment of requirements of morphological andphonological encoding. Structural mapping condition is thus a function that takes asinput all possible interactions and restricts them to only those that make acontribution to structural difference, but it does not guarantee its not beingoverridden by a set of constraints Ф. For example, the phenomenon of agreementis irrelevant to intonational phrasing, and hence any interaction that makesreference to agreement and intonational phrasing involving phonology andsyntax/morphology will be subject to Ф.

2.1 The nature of Ф –the constraints on the general architecture

of language

It has been stated that a range of constraints modulate the interactivedynamics of the linguistic domains or components in Figure 1. It is actuallythe nature and form of these constraints that confer uniqueness upon thecognitive domain of language—this may help see that the interlocking system ofthe architecture in Figure 1 is of the domain of language rather than of thevisual faculty. In this regard, much of what these constraints are supposed tobe has been taken from Jackendoff (2002) who has shown that the interactionamong components of grammar is such that some information in onedomain/component is not accessible to the other or not in a readable formatfor the other domain/component. For instance, syllabification which is a

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matter of phonology is not of concern to syntax. Some more similar cases canbe tentatively drawn up below:

Just as syllabification which is a matter of phonology is not of concernto syntax, generally it is not of concern to semantics as well.

Multiple embedding in syntax is not relevant to phonology which isconcerned about the segments, suprasegments, syllable structure etc.

Hierarchical organization of syntactic structures is not accessible tophonology which has nothing to do with how hierarchical organizationaffects the geometry of structures in syntax. So in this sense, featuressuch as (non)locality, recursion in syntax are not obtrusive tophonology. However, word boundaries and edges of phrases may be relevantto the organization of major (prosodic) phrases in phonology as subjectnoun phrases, verbs, object noun phrases and adjuncts can form major(prosodic) phrases when they are at the edge of a noun phrase or a verbphrase (Selkirk 2006). So it appears that phonology can have access atleast to the lowest level of syntactic organization, if not to thewhole.

Let’s now consider the cases below:

(i) The man left. (ii) The man was at home. He left in the evening.

In such cases as Gillon (2008) has shown, the internal argument can beimplicit, so dropped. It is a matter of semantics as he argues as thisfalls under the domain of invariant features of lexicon and grammar.Hence it implies that this involves lexicon and syntax as well. But thisdoes not have anything to do with phonology per se in that the internalstructure of phonology does not bother about whether an argument isdropped under some interpretative conditions of semantics or not.

Matters of quantification, variable binding in semantics also generallyhave nothing to do with lexicon, but of course with syntax andsemantics.

There is also some information that is not visible to syntax fromsemantics or vice versa as well. For example, many cases of ambiguityand vagueness have nothing to do with syntactic organization. That meanssyntax does not determine how (at least certain cases of) ambiguity is(are) formed in sentences or how vagueness arises in syntacticstructures. This information is certainly mediated by syntax whichorganizes the lexical items in a hierarchical format, but it does not

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have access to how vagueness and ambiguity emerge out of thosestructures. Had it been possible, we would not have found a differencein the following pair of sentences:

(iii) Every man loves a woman. (iv) Every restaurant keeps an executive chef.

Clearly here the sentence (iii) is ambiguous with two scopal readings(one where men vary with respect to a single lady, and another wherewomen vary with respect to different men) and the sentence (iv) is notbecause a single executive chef cannot be kept by every restaurant(maybe in the world or in a city). But has it anything to do with thesyntactic structure? One may certainly propose two different logicalforms (as in Generative Grammar) for a sentence like (iii), but thisdoes not explain why this does not hold in (iv). Clearly, lexicon,semantics and our world knowledge as part of pragmatic reasoning seem tobe involved in this.

In many cases it becomes very difficult to tell apart syntax fromlexicon or morphology (Jackendoff 2007). The boundaries between thembecome fluid. Even if in Figure 1 above five components of language havebeen drawn as distinct, there will be specific constraints that may welldetermine when syntax and say, lexicon become indistinct- they mayoverlap with one another (as in cases like idiomatic expressions such as‘kick the bucket’, ‘take (something) for granted’ which perhaps belongin both lexicon and syntax). Since the architecture in Figure 1 iselastic enough, such fluidity is not banned when languages seem todemand that.

All this seems to point to the direction that there are differential ways inwhich different constraints affect the coordinated interactions among domainsor components of language and one constraint may inhibit interaction betweentwo domains, but enhances or stimulates interaction among others, ofteninvolving one of those two as well. For example, the case with (iii) showsthat even if interaction between syntax and semantics gets blocked by theconstraint, but simultaneously it facilitates interaction between semantics,lexicon and perhaps morphology as well. So it seems that there is a sort ofone-to-many mapping between constraints and the linguistic components ordomains; it can be shown through the following:

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Ci (D1) = ξ1, Ci (D2) = ξ2, Ci (D3) = ξ3, …, Ci (Dn) = ξn … (1)

Here Ci denotes any specific constraint, D1, D2, D3 , … , Dn are linguisticdomains/components (Di ∈ Lc) , and ξ1, ξ2, ξ3, …, ξn denote specific effectsof interactive dynamics among the linguistic domains. Often matters otherthan operational efficiency of processing influence how the constraints (Ф=C1 …Cn) operate; but we do not yet know for sure how constrained the generalarchitecture of language is, not just because exact number of Ф is unknown,but also because matters having to with evolution and the neuro-cognitiveniche in which the architecture of language is ultimately grounded may have(had) an impact on the constraints in Ф and how they work. However, a morenuanced conception of constraints will emerge in section 3.1.

3.On rules, axioms and constraints of grammar and thefaculty of language

Now equipped with the paraphernalia of the general architecture of language asspecified above, we can explicate the nature and form of rules and constraintsof grammar in relation to the faculty of language as conceived of within thegeneral architecture of grammar articulated above. Now the task is tocharacterize the notion of rules and principles of D1, D2, D3, … , Dn, given thegeneral architecture of language above. But what is the relation between suchrules and principles and the set of constraints Ф= C1 …Cn? Let’s state thefollowing axioms:

Axiom 1:

Let there be a set of linguistic domain functions κ = LD1 … LDk such that foreach Di there is some set πi ⊆ κ and LD: α → β where α is a graph in Di and β isan n-tuple of binary relations <R1 … Rn> for Di.

Axiom 1 is a descriptive statement of the constitutive elements of linguisticcomponent/domains each of which incorporates some subset of (linguisticdomain) functions (κ = LD1 … LDk) for the constitutive relations of theformative elements in each linguistic component/domain. In other words, whatAxiom 1 ensures is that for each linguistic domain out of D1, D2, D3, … , Dn

there must be a subset of κ and thus there will be a subset π1 for lexicon,another π2 for syntax, π3 for morphology, π4 for phonology and π5 for semantics

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such that π1… πn ∈ (𝒫 κ) (the power set of κ). Since it is not necessary thatthere has to be a symmetric difference among π1… πn , some of π1… πn may be sharedamong D1, D2, D3, … , Dn. Because of this, there might be many parallels inrules and structures among D1, D2, D3, … , Dn. This is what has been emphasizedby Anderson (2011). It should be made clear that the axiomatic requirementsfor different but partially overlapping LDs in the linguisticcomponent/domains does not carry any assumption that all the differentcomponents/domains in a general architecture of language are also ontologicallydifferent. As Cann, Kempson and Wedgwood (2012) distinguish levels of analysis inlinguistic descriptions from levels of representation as the former is orientedtowards empirical adequacy of analyses while the latter pertains to adistinction in ontology among linguistic domains, there is no presuppositionin the present context that different linguistic components are eitherontologically different or level-wise distinct. This is because thedistinction between levels of analysis and levels of representation cuts across the generalarchitecture of language in Figure 1 in that form as ontologically distinctfrom meaning is distributed across a number of linguistic component/domains—namely, syntax, lexicon, phonology and morphology, but meaning is restrictedto semantics. And at the same time, syntax, lexicon, phonology, morphology andsemantics are not different levels of analysis, since the concept of anessentially uniform LD across the linguistic components/domains is juxtaposedwith a difference in the formative elements and their relations ofconstitution in each linguistic component/domain. The linguistic domainfunction maps a graph structure onto an n-tuple of binary relations <R1 … Rn>such that the graph can vary in structure from one linguistic domain toanother, and similarly, the binary relations R1 … Rn can also vary from onelinguistic domain to another. Hence, for syntax, we might need a treestructure in α and dependency or/and constituency or/and command relations (orwhatever the case maybe) in β. An example may illustrate this properly.Suppose that we have a sentence ‘John knows that Mary is beautiful’; in termsof an LDi: α → β in syntax, α can be taken to be a tree graph as schematizedbelow and β can be a 2-tuple of binary relations R such that we have <R1, R2>where R1 = <(NP, VP), S>, <John, NP>, <(knows, CP), VP>, <that, C>, <Mary,NP>, <is, V>, <beautiful, AP>, <(is, beautiful), VP> is a syntacticconstituency relation and R2= <John, knows>, <that, knows>, <beautiful, is>,<Mary, (is, beautiful)>, <CP, knows> is a dependency relation in which thefirst element in each pair depends on the second. Here NP=noun phrase, VP=verbphrase, CP=complementizer phrase, V=verb, AP=adjective phrase,C=complementizer and S=sentence.

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Figure 2: A tree for the sentence ‘John knows that Mary is beautiful’

Similarly, for lexicon, we may need a tree structure or a lattice for α andconceptual relations or/and relations of qualia structures (see Pustejovsky1995) or/and relations of features, attribute-value pairs etc. for β; thus forthe sentence as depicted in Figure 2, we need lexical items—‘John’, ‘Mary’,‘know’, ‘be’, ‘beautiful’—each of which can be characterized in terms ofanother LDj: α → β such that α is tree graph of the form shown below, β is a2-tuple of binary relations <R1, R2>.

S

NPJohn

VP

Vknows

CP

Cthat

S

NPMary

VP

Vis

APbeautiful

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Figure 3: A tree for the noun phrase ‘John’

R1= <John, object>, <John, name> is a conceptual relation containing binarypairs and R2= <John, FF>, <John, CF>, <John, AF>, <John, TF> is a qualiarelation specifying formal features (FF) of ‘John’ (‘John’ is animate and a humanbeing), constitutive features CF (John’s physical features and appearances), agentivefeatures AF (John’s personal history and his personal details) and telic features TF(characteristic activities and actions of John). Similar LDs of the same indexj can be used for other lexical items as well. For phonology α would includetrees or lattice and β will be relations of articulatory, auditory, perceptualfeatures in association with dependency or constituency roles. Thus adifferent LDk: α → β for phonology will include a mapping for each of thelexical items in ‘John knows that Mary is beautiful’; so ‘John’, for instance,will have a α that will look like

NP N John

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Figure 4: A tree for the syllable structure of ‘John’

and β will be a 2-tuple of binary relations <R1, R2> such that R1= <John,SF>, <John, AP> is a relation that specifies the segmental features (SF) of thesegments of ‘John’ and the articulatory-perceptual features (AP) of the syllable of‘John’ and R2= < John, σ>, <dʒ, Onset>, <ɒ, Nucleus>, <n, Coda>, <ɒ, n,Rhyme> is a combinatory relation for the syllabic elements of ‘John’.Importantly, within phonology we may also need another LD: α → β of the sameindex k that will determine how major (prosodic) phrases and intonationalphrases can be assigned to the sentence ‘John knows that Mary is beautiful’ asa whole. But for this, a reference to the syntactic LDi may be necessary;hence the LD for syntax (LDi) and the LD for phonology (LDk) can be partiallyshared across the interface linking syntax and phonology if and only if it iscompatible with constraints that determine how much from either phonology orsyntax (what subset(s) of LDi and what subset(s) of LDk) can be mutuallyshared. To move on, similar considerations involving another LD incorporatingfeatures and combinations of morphemes will be required for morphology suchthat trees or lattice would serve what α is supposed to be and β would berelations between stems, infixes, prefixes and suffixes. We shall leave outthe details for this because essentially similar principles apply here too.Finally, for semantics, α would be a graph as shown below.

σ (John)

RhymeOnset ʤ

Nucleus ɒ

Coda n

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Figure 5: A type-logical tree for the sentence ‘John knows that Mary isbeautiful’

And β will represent relations of semantic tiers (in Jackendoff’s (2002)sense) or/and relations of cognitive structures/schemas (as in CognitiveLinguistics) or/and logical representations in set-theoretic structures. Thiswill yield a 3-tuple of binary relations <R1, R2, R3> such that R1= <‘Johnknows that Mary is beautiful’, DT>, <‘John knows that Mary is beautiful’, MT>,<‘John knows that Mary is beautiful’, RT> is a relation that specifies thesentence here in terms of three tiers: the descriptive tier (DT) specifies thatthere are two linked states one of them has ‘John’ as an object and the otherhas ‘Mary’; the macrorole tier (MT) specifies that ‘John’ is an experiencer of astative proposition which contains Mary as the theme and the referential tier (RT)specifies that there are two referential NPs, namely, ‘John’ and ‘Mary’ havingdifferent indexes and are dependent on the event indices of ‘know’ and ‘be

t

e e t

t (e t) t

t t t

e e t

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beautiful’ respectively, and R2=<‘John knows that Mary is beautiful’, C-schema>, <John, Trajectory/Focus>, <knows, Process>, <‘that Mary isbeautiful’, Landmark/Ground>, <Mary, Trajectory/Focus> is a relation ofcognitive/conceptual schemas (C-schema) and R3= <John, a set of individualswho know that Mary is beautiful>, <(John, ‘that Mary is beautiful’), a set ofordered pairs of individuals who know and propositions known>, <Mary, a set ofindividuals who are beautiful> is a relation of set-theoretic membership. Insum, all this characterization is independent of any (specific) linguisticformalism (very much in the spirit of Miller 1999) and at the same timeindependent of any specific language as well. The exact graph (whether it is atree or a lattice) in α and the exact relations (the tuples in the relations)in β may vary across and within languages for various linguistic phenomena.

Axiom 2:

Rules for linguistic phenomena across and within languages will here bemappings of the form:

ψ: < LD1, … ,LDk> → < LD1, … ,LDm> when it is not necessary that k = m.

Axiom 2 is, in fact, a vindication of the point raised by Kac (1987) andKracht (1998). As specified by the Axiom 2, rules for linguistic phenomena areof a sufficiently general character. The question of linguisticuniversals/principles of universal grammar versus linguistic variation becomesneutralized here as linguistic rules in the current framework involveoperations on tuples of linguistic domain functions which have a generalcharacter, and thus this conception is different from the view of Keenan andStabler (2010) who focus only on the structural universals of language withoutany architectural import inherent in such structural universals. Butsimultaneously, the range and domain of these linguistic domain functions arerelative to linguistic domains and the linguistic phenomena themselves acrossand within languages. An example will perhaps make this clearer. Let’s takethe case of Wh-questions. It is perhaps one of the most investigatedlinguistic phenomena in generative grammar (see for a discussion, Aoun and Li2003). Superiority effects in both Wh-movement structures and non-movement Wh-structures have been observed. Some examples from English are the following:

1. (a) Who saw what?

(b) *What did who see?

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2. (a) Who came after what?

(b) *What did who come after?

3. (a) Who did you convince to see what?

(b) *What did who convince who to see?

Such cases abound in languages like Lebanese Arabic etc, as Aoun and Li (2003)show. Such Superiority effects are associated with principles like Subjacencyor Attract Closest or Minimality Condition on Movement the operation of all ofwhich consists in movement of an item to the closest possible target. However,such cases can be represented as a mapping from some tuple <LD1,… ,LDi> (withthe LD1,… ,LDi from syntax, lexicon and perhaps morphology) onto another tuple<LD1,… ,LDj> when i ≠ j and LD1,… ,LDj are within syntax and semantics. Treegraphs with the associated constituency/dependency relations from <LD1,… ,LDi>will be mapped onto the tree graphs with the associateddependency/constituency relations and conceptual relations from <LD1,… ,LDj>with the smallest edge distance (relative to those trees with ungrammaticalstrings in a surface tree) between two vertices V’ and V’’ when V’ representsa Wh-occurrence and V’’ represents what V’ depends on (a verb or prepositionetc. as in dependency theory) or the co-indexed expression of that Wh-occurrence (resumptive pronouns, for example). It can be noted that thischaracterization is independent of any assumptions about movement. Whateverdependency/constituency relations are associated by a given LD with treegraphs are specific to that LD.

But this characterization leaves open other possibilities. Pesetsky (2000) hasargued that Superiority effects do not obtain in the case of Which-phrases.

4. (a) Which police officer raided which house?

(b) Which house did which police officer raid?

On the other hand, Hofmeister et al. (2013) have shown that Superiorityeffects do not obtain in many potential cases of the following and thecriteria pointed out above are flouted:

5. What did who read?

6. What rules should who follow?

Cases like this (4-6) will have different LDs in the tuple <LD1,… ,LDj> fromsyntax and semantics when ψ maps the tuple <LD1,… ,LDi> onto < LD1,… ,LDj>.

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The status of LDs for cases in (4-6) is just like that of LDs in (1-3). Thesame point can be elucidated with another example. Beck (1996) has argued thatquantified structures can block LF (Logical Form) movement of wh-elements,other quantifiers and also restrictive elements of Determiner Phrases (thoughBeck (2006) has provided a different account of such intervention effects onthe grounds of requirements of information structure) as in the generativetradition LF is postulated to be the (covert) level where syntacticcontributions to meaning are represented. However, the data are shown below in(7) and (8) where at the level of LF ‘niemand’ blocks the movement of ‘wo’ in(7) and so does ‘nicht’ to ‘wer’ in (8):

(7) *Wen hat niemand wo gesehen?

whom has nobody where seen

‘Where did nobody see whom?’

(8) * Was glaubt Hans nicht, wer da war?

what believes Hans not who there was

‘Who does Hans not believe was there?’

According to Beck, such intervention effects of quantificational structurescan also explain quantifier scope in German. This kind of linguisticphenomenon can also be represented the following way. There will be a mappingψ from some tuple <LD1,… , LDi> (the relevant LD1,… ,LDi being from syntax,lexicon and perhaps morphology) onto another tuple <LD1,… ,LDj> when i ≠ j andthe relevant LD1,… ,LDj are from syntax and semantics. Tree graphs with theassociated constituency/dependency relations from <LD1,… ,LDi> will be mappedonto the tree graphs paired with associated dependency/constituency relationsand conceptual relations from the tuple <LD1,… ,LDj> such that some LD fromthe tuple <LD1,… ,LDj> will have in β conceptual/cognitive structures notencoding/representing bindings of variables represented by Z (Z = wh-elements, other quantifiers and also representations of restrictive elementsof Determiner Phrases (DPs)) iff Z is a vertex in a tree graph in α and Y (=quantified elements) is another vertex in the same tree graph and a relation R(‘precedes’) holds between Y and Z (YRZ).

If there are other languages that also fall in line with such rules for thesame phenomenon, the same kind of mapping as above will thus obtain. To drivehome the point made above, the status of LDs in (7-8) is no different fromthat of (4-6) or (1-3) in a way that there is distinction between principles

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and rules as it may be the case in generative grammar. From anotherperspective, the linguistically relevant cut is not between language-universalrules and language-specific rules but rather among rules of different types ofgenerality. It is just rules all the way but of different types of generalityindirectly determined through the constraints (on the general architecture) bythe influence of linguistic function, representation and processing asdetailed in Mondal (2012). And this is ensured by the mapping ψ in Axiom 2that is general enough for all LDs.

Axiom 3:

An I(χ) among D1, D2, D3, … , Dn ∈ Lc is a set of ordered pairs <a, b> ∈ I(χ)such that a is a member of the set of ψs and b is a member of 𝒫(Ф), andtherefore, I(χ) = <a1, b2>, . . . , <an, bn>.

Axiom 3 elaborates on the stipulation made in the second section. It makessure that any interaction I(χ) in the architecture in Figure 1 must conform tothe stipulation by having every rule paired with the relevant constraints fromC1 …Cn. In other words, every rule for any linguistic phenomenon must satisfya (sub)set of constraints that determine the form of interactions among thelinguistic domains. Thus, for example, a rule for assimilation of twosegments, say, x and y in a word or across words to be defined at thesuprasegmental level (if we posit one in our LD for phonology) will be theform of a mapping of type ψ (from Axiom 2) some tuple <LD1,… ,LDi> (with theLD1,… ,LDi from phonology and lexicon) onto another tuple <LD1,… ,LDj> when i ≠j and LD1,… ,LDj will include morphology. Thus, tree graphs with the associatedsegmental and syllabic constituency/dependency relations from <LD1,… , LDi>will be mapped onto the tree graphs with the associateddependency/constituency relations and morphological relations from <LD1,

… ,LDj> as phonological processes may well affect morphological processes (asin English plural morphology manifest in the distinction between roses,boxes…,boys, cows … and cats, laps … grounded in the phonologicalassimilation of voicing/non-voicing across morphemes). What is important tonote here is that the relevant rule for assimilation of the two segments x andy may affect meaning, in so far as the concept of plurality is different fromthat of singularity. But any process of (re-)syllabification following on fromphonological assimilation (when, for example, the word ‘handbag’, undergoingassimilation, turns into /hæmbæg/ and may thus be (re-)syllabified as/hæm.bæg/ or /hæmb.æg/) may be irrelevant to semantics and is thus inconsonance with some subset from 𝒫(Ф). Another interesting example can beprovided from the phenomenon of raising/control to illustrate how Axiom 3

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works in the context of constraints that operate on the general architectureof language. Here are some examples:

(9) John seems to be worried about his wedding.

(10) Ray is likely to retire soon.

(11) Steve believed the guy to have justified his case.

(12) Mary loves playing baseball.

(13) John tried to flee to France to pursue his passion for art.

(14) We have asked him to step down.

The examples (9-11) are cases of raising whereas (12-14) are examples ofcontrol. The most significant and essential criterion that helps make out therelevant difference is that in all cases of raising, an argument (whether theexternal argument or the internal argument) of the embedded predicate is notseen where it is theta-marked (or interpreted) but appears elsewhere in thematrix clause (either in the subject position or in the object position).Thus, (9-10) are cases of subject raising in that the subject ‘John’/’Ray’ isinterpreted in the theta position of the embedded predicate ‘be worried abouthis wedding’/’retire soon’ but in fact appears in the matrix clause. (11) is acase of object raising as the object has been displaced from where it shouldbe interpreted. Hence in (11) it is not the guy who Steve believed; rather,the object of Steve’s belief is the proposition that the guy (has) justifiedhis case. On the other hand, (12-14) exemplify typical features of controlsince the relevant argument of the embedded predicate is interpreted wherethey should be but this interpretation or theta-marking of the relevantargument is distributed across all the embedded predicates along with thematrix predicate. It looks as if there is a kind of sharing of the sameargument by many predicates across clause boundaries. Because of this propertyof control, a null argument PRO is used and indexed with the (noun) phrasethat is overtly present. Thus, in (12) ‘Mary’ is an external argument of both‘love’ and ‘play’ and in (13) ‘John’ is an external argument of ‘try’, ‘flee’and ‘pursue’. The example (14) illustrates object control as ‘him’ is also anexternal argument of ‘step down’ aside from being the internal argument of‘ask’. What these examples suggest is that control is the obverse of raisingand vice versa. This is because control consists in sharing of the sameargument or (a set of arguments) among a number of predicates across clause

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boundaries whereas raising involves sharing of many forms with the samemeaning.

(15) (a) There are likely to be some volunteers in the hall.

(b) *There hope to be to be some volunteers in the hall.

(16) (a) They believe close tabs to have beenkept/*placed/*maintained on her movements.

(b) *They convinced close tabs to be kept/placed/maintainedon her movements.

((16) is taken from Postal 2004)

Let’s consider the examples in (15-16) as well to see the point. In (15a) araising construction can easily go with an expletive while a controlconstruction cannot as in (15b). Besides, (16a) shows that raising is fullycompatible with an insertion into an idiomatic chuck, whereas control is not,as (16b) indicates. If so, this means that control disallows or resists anyintegration or coalescence of further forms from syntax or lexicon ormorphology when a single form can be semantically mediated by many predicates,thereby leading to a proliferation of semantic links. That is, semantics canafford to have a multiplicity of meanings linked via a single form but doesnot tolerate this on the part of any of the formal components—syntax, lexicon,morphology. This is similar to what happens in cases of semantic ambiguity.For example, a sentence ‘John left his university’ can have two meanings: (i)John physically moved out of the physical boundaries of the universitybuilding and (ii) John finished his studies at his university. As wasdiscussed in section 2.1, this is a constraint at the interface between syntaxand semantics when semantics goes its own way in having more meanings than isvisible in syntax. The interface in such a case cannot extract much fromsemantics in so far as syntax cannot access many LDs in semantics. This isexactly what happens in the case of control in that semantics projects manyLDs for cases in control many of which are not accessible to syntax at allbecause of an interface constraint, which is a part of Ф or 𝒫(Ф). Whatraising, on the other hand, reveals is that this specific constraint ∈ Ф or∈ 𝒫(Ф) has a counterpart too, but in the opposite direction (note that anyconstraint can potentially be bidirectional in that if something is notaccessible from X to Y it is quite likely that something is also notaccessible from Y to X). That is, linguistic form as conceptualized in the

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current context is distributed among syntax, lexicon, morphology andphonology, and any duplication or proliferation or spreading of forms whenkeyed to a single meaning can have a balancing effect on the architecture ofthe language faculty when its obverse already exists. Hence raising allows fora proliferation or integration of further forms with no concomitantproliferation or spreading on the part of semantics. This explains whyreduplication or agreement marking across a number of parts of a singleconstituent or constituents is pervasive in natural language (consider, forexample, the sentence ‘These boys are very efficient volunteers’). Thus, Axiom3 helps determine that whenever we have a rule for raising/control as part ofψ, the pair <ψ, b> will make sure that the rule for raising/control isconsistent with relevant members of 𝒫(Ф) which will block some LDs or somesubsets of LDs from being mapped onto some others. This can be schematizedbelow.

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Figure 6: How Axiom 3 plays itself out in control/raising

Figure 6 shows how Axiom 3 may work in the case of control/raising. Only asubset of an LD from semantics will be mapped onto syntax for cases of controlsuch that some subsets of LDs that specify that an argument X—which is anargument of some predicate Y— is also an argument of other predicates will beblocked from being mapped onto syntax. That is, only the part of the LD thatspecifies that X is an argument of Y will be mapped onto syntax and the restof the stuff will remain as it is in semantics. This is consistent with 𝒫(Ф).That is why we do not have a sentence like ‘John tries John doing the work’.Similarly, in raising some subset of an LD (or LDs) from a union of syntax,lexicon and morphology—especially the part associated with the form displaced—

ψi = Rule(s)

for Control

Raising

< ψi, bi >when bi ∈𝒫(Ф)

LDj from Semantics

LDk from Syntax Lexicon Morphology

Formation of a Subset of LDj

Formation of a Subset of LDk

Syntax

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will not be mapped onto semantics, thereby yielding a raising construction.This is also compatible with 𝒫(Ф). Compatibility with 𝒫(Ф) is indicated withcurved arrows in Figure 6 oriented toward LDj (in semantics) and LDk (insyntax).

As it stands, the three axioms in the current framework encapsulateformalizations of rules, linguistic domain functions, interaction among thelinguistic domains and the relevant relations between them. From this itfollows that axioms are far more general in character than rules, constraintsor linguistic domain functions. Hence, in the present schema rules aredifferent from constraints and constraints and rules are in turn differentfrom axioms.

3.1 The relationship of rules with the general architecture oflanguage

So far we have not been able to look into the precise nature of therelationship between the rules of syntax, semantics, morphology and phonologyalong with the constraints, and the general architecture of the faculty oflanguage as schematized in Figure 1. Even if the three axioms above have shownin some ways the general nature of the relationship between rules, constraintsand linguistic domain functions, this needs a bit of more precision. This willbe done with the postulation of two theorems to be presented below.

Theorem 1:

If Ci (Dn) = ξn , then any ξn = <I(χ) , ψ>.

Proof: If ξn is the outcome of the application of a constraint Ci, then Ci =<Dn, ξn > | Dn is a linguistic domain/component and ξn is the outcome ofapplication of Ci. Then from this it follows that Ci = <Dn, <I(χ) , ψ>>. Ifthis is the case, it is necessary that Ci (D1) = <I(χ) , ψ>1, … , Ci (Dn) =<I(χ) , ψ>n (by following the formulation in (1)). If so, then for each Di

there is some set of ordered pairs <ψ, b> : <ψ, b> ∈ I(χ) paired with ψ whichis a mapping from a tuple of LDs onto another tuple of LDs (from Axiom 2 &3).So we have now < <ψ, b> : <ψ, b> ∈ I(χ) , ψ>. The fact that for every Di therewill be some πi ⊆ κ when κ = LD1 … LDk (from Axiom 1) is ensured by ψ. And forthat matter, since different π1, …, πi will span over different D1, D2, D3, … ,Dn , it must be the case that different subsets of Ф will be at play given Ci

(D1) = <I(χ) , ψ>1, … , Ci (Dn) = <I(χ) , ψ>n. Therefore, <I(χ) , ψ> must bethe outcome of application of Ci as long as <ψ, b> : <ψ, b> ∈ I(χ) designates

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the procedure of applying the rule ψ conditional upon the relevantconstraints, and ψ is the application of the rule.

Theorem 2:

Every ψ is closed under an n-tuple function Fn on I(χ).

Proof: If Fn is an n-tuple function Fn, then Fn(I(χ)) = ψ. It follows that Fn =<I(χ) , ψ>| every <I(χ) , ψ> is a member of Fn. Since every <I(χ) , ψ> ∈ ξ(from Theorem 1), then Fn = ξ. Let’s then assume that there is some ψ’ that isnot closed under Fn on I(χ). If so, then ψ’ is not in the range of ξ as well.But we know from Axiom 1 that for every Di there will be some πi ⊆ κ when κ =LD1 … LDk and ψ’ by being a mapping between tuples of LDs must have LDs ∈ πi

for D1, D2, D3, … , Dn ∈ Lc. On the other hand, if ψ’ is not in the range of ξ,ψ’ is not in the domain of I(χ) (from Axiom 3) as well and contains tuples ofLDs for some H∉ Lc. This leads to a contradiction. So every ψ must be closedunder an n-tuple function Fn on I(χ).

Corollary (from Theorem 1 & Theorem 2):

Any warped state of the architecture of the language faculty (due to the application of someconstraint(s) ) is identical to some relation ℜ containing ordered pair(s) of linguistic interaction (I(χ))and rules (ψ).

What this means has far-reaching consequences deriving from the nature ofelasticity of the general architecture of the language faculty presented here.In fact, the corollary above provides scaffolding for the elasticity of thegeneral architecture of the language faculty. Some examples can clarify whatis at stake here. Let’s take the case of subject extraction. Extraction fromsubjects is generally banned (Hornstein, Lasnik and Uriagereka 2006). Thus(17-18) are not grammatical.

(17) *Who did stories about upset him?

(18) *Who did shadows of lurk behind the tree?

Chaves (2013), after surveying a huge literature on subject extraction, comesto the conclusion that subject extraction is rare yet possible. He hasprovided the following fairly acceptable examples, among many others, in orderto argue for his case. In particular (22) shows that extraction from a subjectclause is also possible.

(19) Which disease will the cure for never be discovered?

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(20) Which question will the answer to never be known?

(21) Which problem will a solution to never be found?

(22) There are people in this world that – for me to describe asdespicable – would be an understatement.

He goes on to argue for a parsing principle-based account of the widely variedcases of extraction from subjects. That is, expectation of no form-meaningmismatch in subjects is the primary parsing principle that, he believes, canaccount for the diverse range of cases of subject extraction across languages,by allowing for degrees of acceptability. Be that as it may, this can have astraightforward and much simpler account in terms of what the corollary abovespecifies about the elasticity of the general architecture of the languagefaculty. In fact, such empirical data can provide a strong support for theelastic property of the general architecture of the language faculty.

Here is how. If the elasticity of the general architecture of the languagefaculty emanates from some constraints imposed on the interaction among thelinguistic components, such elasticity ensures that some linguisticcomponent(s) may not have access to representations in some other linguisticcomponent(s). Hence extraction from subjects, in general cases, derives from aproliferation or spreading of forms with no concomitant proliferation orspreading on the part of semantics—which explains why resumptive pronouns areoften used in some cases of extraction. That is, some subset of an LD (or LDs)from a union of syntax, lexicon and morphology is not mapped, as was shown forthe phenomenon of raising above, onto semantics, semantics not being privy toall that happens in syntax (by virtue of 𝒫(Ф)). But such elasticity due tothe blocking of semantics from partaking of syntactic representations does notseem to be generally valid in English (as in 17-18) but is possible in (19-22)and other languages such as Russian, German, Hungarian, Hindi etc., as Chavesmaintains. Extraction from adjuncts enjoys the same status as subjectextraction—that is—it is not valid in general cases but is acceptable in manyother (as in ‘What did she move out to buy some stuff from_?’) (See fordetails, Truswell 2011). Overall, whenever elasticity in the generalarchitecture of the language faculty does not obtain (due to form-meaningconvergence), cases of extraction from subjects, adjuncts (and alsocomplements) do not thereby follow. But when elasticity holds in the generalarchitecture of the language faculty, extraction from subjects, adjuncts (andalso complements) occurs and this is certainly a matter of some linguisticinteraction (I(χ)) being related to rules (ψ)—which is what the corollary

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states. Any absence of elasticity in the general architecture of the languagefaculty reinforces form-meaning convergence, ensures transparency among thelinguistic components, and can thus be anything other than a pairing oflinguistic interaction (I(χ)) and rules (ψ). That is, an absence of elasticityin the general architecture of the language faculty can simply be somelinguistic interaction (I(χ)) among the linguistic components (which may wellinvolve a null element from 𝒫(Ф), given that I(χ) is a set of ordered pairs<ψ, b>, or some rule(s) (ψ)—which is exactly the case when extraction isdisallowed.

More interestingly, elasticity occurs not merely for strictly linguisticreasons but also for projecting the system of linguistic axioms andconstraints onto the cognitive substrate, as detailed in Mondal (2012). Thus,such projection realizes/instantiates what Dascal (1992) calls ‘psycho-pragmatics’ which also provides a basis for ‘socio-pragmatics’, because thiskind of projection is for mental uses of the linguistic system (a matter ofpsycho-pragmatics) as well as for a mental grounding of the linguistic systemto be exploited with respect to socio-cultural contexts and settings (a matterof socio-pragmatics). Important to note in this connection is the point thatsuch projection is intentionally done by humans, and is co-intensive with theintentional grounding of the system of linguistic axioms by human beings whorelate any operation in the general architecture of the faculty of language toa system of rules, axioms and constraints. Thus, this extends the domain ofwhat Dascal calls psychopragmatics to mental uses of the linguistic system ina more general sense (not merely in reasoning, problem solving or dreams). Itmay also be noted that the intentional projection of the linguistic system ofaxioms and constraints may be interspersed with the interaction (I(χ)) amongthe linguistic components at some sub-personal or non-intentional level.Another advantage that comes out of this is that any reference to any kind oflogical form in pragmatic inferences that has to be mapped onto the semanticsystem for semantic interpretation is redundant. All pragmatic processes—whether primary or secondary (see Recanati (2004) for details)—can berealized/instantiated by the projection of the system of linguistic axioms andconstraints onto cognitive processes at large. Hence cases of extraction fromsubjects, adjuncts (and also complements) can line up with the recruitment ofparsing principles derived from cognitive processes to which the system oflinguistic axioms and constraints is intentionally projected.

Additionally, another linguistic evidence for the elastic nature of thelanguage faculty may also come from the nature and form of non-active voicesin natural language. Middles and passives are two kinds of non-active voices

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which appear to be distributed in formally different ways across languages(Alexiadou and Doron 2012). As Alexiadou and Doron argue, the fundamentaldistinction between middles (as in ‘This fruit cuts easily’) and passives (‘hewas killed (by someone)’) is that middles allow but do not require theparticipation of the agent argument, while passives require the participationof the agent argument. The distinction is formally marked in languages likeHebrew but unmarked in Greek. This can fall straightforwardly out of theelastic nature of the language faculty in that the participation of the agentargument is a semantic requirement coming from the semantic component that issubject to a constraint from 𝒫(Ф), and if so, this semantic requirement maynot be visible to syntax. This provides a key to the resolution of the puzzleabout middles versus passives across languages. That is, if due to theelasticity in the architecture of the language faculty a semantic demand forthe participation of the agent argument is not available in syntax, what getsformed is a middle; passives appear when elasticity does not obtain in thespecific case of non-active voice marking. Therefore, if elasticity in thearchitecture of the language faculty drives the intentional projection of thelinguistic system onto cognitive processes, thereby leading to psycho-pragmatics and socio-pragmatics, formation of middles may readily engagepragmatic reasoning and inferential processes because of the absence of theform in syntax that can represent the agent argument. From this it does notcertainly follow that an absence of elasticity in the architecture of thelanguage faculty in a particular linguistic phenomenon does not engageprocesses of pragmatic reasoning and inferences. Rather, they may be invokedin a state in which the intentional projection of the linguistic system ofaxioms and constraints is interspersed with the interaction (I(χ)) among thelinguistic components at the sub-personal or non-intentional level. In fact,this is exactly what happens in a case in which semantic differences do notfall out of syntactically relevant structural variations, as in intensionalemotive constructions, for example, that involve intensional elements usedwith emotive predicates (see for details, Mondal 2013). In this sense,pragmatic inferences need not be rules in the sense specified by ψ (in Axiom1), but rather are instantiated by the intentional projection of the system ofrules, constraints as governed by the axioms.

To sum up, Theorem 1 has tried to encode an intimate relationship betweenconstraints on the general architecture of language and interaction among thelinguistic domains with rules. Thus, constraints in the form of functions giverise to ordered 3-tuples of linguistic domain functions (LDs), linguisticinteraction (I(χ)) and rules (ψ). This follows straightforwardly from the

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nature of constraints, the substance of linguistic domains and the form ofinteraction among these domains. Theorem 2 has pulled the boundaries of alllinguistic rules tight by having them all bound within I(χ) and ultimately, bythe constraints on the general architecture of language. Overall, this helpsproject a precise model of the exact relations between linguistic rules,constraints and interaction among linguistic domains. But some questions stillremain. Does this all exhibit a transparent relation between the operations ofthe general architecture of language and linguistic rules of syntax,semantics, morphology and phonology within the axioms of grammar? The nextsection will explore this question.

4.On a transparent translation between the operationsof the general architecture of language andlinguistic rules, axioms of grammar

The third goal as stated in the first section raises the issue ontranslational transparency between the operations of a general architecture oflanguage and (linguistic) rules of syntax, semantics, morphology andphonology. In fact, Chomsky’s (1975) work on an axiomatic system for rules ofgrammar in a system of levels of representation was not exactly orthogonal toan architecture-laden specification in terms of levels of details(computational, algorithmic and implementational levels) (Foster, 1992). Whatis in focus is that this issue has been raised in connection with thedemonstration by Kracht (1998) that translation between logics and grammar canbe achieved without any liaison with any architecture of a linguistic theoryby means of elimination of any principled distinction between the principlesof grammar and linguistic rules. The present work extends, much lessmitigates, this possibility by showing that it can be achieved even if thereis an architecture of grammar provided that the architecture is general enoughto allow for a translation between the operations of the architecture and therules of grammar (in the sense of rules of syntax, semantics, morphology andphonology). In fact, type transparency between a grammar and a parser hasalways been a moot point since the advent of generative grammar (Berwick andWeinberg 1984; Stabler 2010). Even if the issue of translational transparencybetween the operations of the architecture of the faculty of language andrules of grammar is tangential to that between a grammar and a parser, thereare significant differences. Translational transparency between the operationsof the architecture of the faculty of language and rules of grammar is a moregeneral and broader notion than that of type transparency between a grammar

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and a parser. Undoubtedly, the presence or the lack of type transparencybetween a grammar of the language faculty and a parsing grammar is tinged witharchitectural constraints on operations as it has been in the generativetradition. The operations involved in parsing (just as those in languageproduction) are just a subset of the entire range of operations a generalarchitecture of language can yield to as in the present framework; therequirement and operations of parsing can be easily stated in the form of aninteraction I(χ) given that specific ψ is defined for that particularinteraction. Hence, translational transparency between the operations of ageneral architecture of language and (linguistic) rules of syntax, semantics,morphology and phonology is of a more substantial nature in that this kind oftranslation is not just about specifying structural universals of language inthe sense of Keenan and Stabler (2010) or about finding out a homomorphismbetween a grammar of the language faculty and a grammar for processing.Rather, the issue is about whether the operations of a general architecture ofthe faculty of language can be, without any loss in conceptual substance andrepresentational adequacy, translated into axioms and rules of grammarcovering syntax, semantics, morphology and phonology. The present work aims atachieving this not certainly at the expense of any blindness to linguisticphenomena.

At this point, it should be borne in mind that when we talk about atranslational transparency between the operations of a general architecture oflanguage and (linguistic) rules of syntax, semantics, morphology andphonology, in an obvious sense we do certainly mean that the operations of ageneral architecture of language are constituted by the (linguistic) rules ofsyntax, semantics, morphology and phonology. However, in a more relevant andperhaps deeper sense, we also mean that a translation of the operation of thearchitecture of the language faculty into a system of rules, axioms andconstraints is at best a description. The description is intentional in thesense that the system of rules, axioms and constraints is not represented orinstantiated in the architecture of the language faculty any more than thebinary numerical system is represented or instantiated in the decimal systemwhen translated from it. The system of axioms and constraints is intentionallygrounded by us—human beings, whenever any operation in the generalarchitecture of the faculty of language is related by human beings to a systemof rules, axioms and constraints all of which derive from, insofar as they arerelated to the language faculty, the nature and form of the language faculty.More on this will be spelled out in the sixth section (section 6). But thishas not been a practice in theoretical linguistics; there are in fact two

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extreme positions that can be singled out. One extreme is the positionespoused in mainstream Generative Grammar which posits rules and constraintswhich are represented in the language faculty (Chomsky 1980, 1995) and theother extreme position is visible in frameworks like Head-Driven PhraseStructure Grammar (Pollard and Sag 1994) which have completely dissociated thesystem of signs from any architecture of the language faculty, thusmaintaining a neutrality with respect to issues of realization of the systemof grammar in the language faculty. Lexical Functional Grammar (Bresnan 2001)is pitched in a somewhat similar fashion, though Lexical Functional Grammar atits foundational core has tried to stick to an homomorphism between the systemof rule types of grammar and processing functions in the mind (Bresnan 1978).The only difference is perhaps Jackendoff’s Parallel Architecture (Jackendoff2002); but the system of rules and constraints is non-intentionally representedin the Parallel Architecture of the language faculty. There is no way ofdenying that there may exist crippling problems coupled to the duality, orrather the tension between two different ontological levels of an infinitelanguage and a finite representation of grammar in the mind/brain (see fordetails, Langendoen and Postal 1984; Postal 2004), the present work attemptsto unify the significant aspects of the relation of the system of grammar tothe language faculty in a kind of meta-theoretical or trans-theoretical mannerbut without at the same time getting bogged down in impregnable puzzles andinconsistencies that may lie at the thread connecting the system of grammar tothe language faculty. Therefore, the aim is not to replace current theories;rather, the aim is to place them in the right space.

5.Implications for linguistic theoryWith this, we can now move on to thrash out the linguistic implications givena translational transparency between the operations of a general architectureof language and (linguistic) rules of syntax, semantics, morphology andphonology. The relevant consequences straightforwardly follow on from thistranslational transparency. If such translational transparency is to beexpected, perhaps it is then futile to argue for a rigid configuration of anypostulated architecture of the faculty of language since imposition of anarrowly constrained particular directionality on the postulated configurationbars otherwise possible configurations and directionalities. Given the issueson linguistic explanation (see for details, Moore and Polinsky 2003), theseconcerns are not perhaps too off the mark. Given a proliferation of differentarchitectures of grammar/language in the present situation (Jackendoff 2002),it behooves us to rethink the substantive issues with a view to understanding

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what is at stake. The three goals set out in the first section clearly cordonoff the relevant matters of substantive and formal correspondences. To whatextent should we demand a correspondence between substantive adequacy(faithfulness in accounting for linguistic phenomena) and formal explicitness(formalization in linguistic formalisms)? As aptly pointed out by Kracht(1998), issues of formalization are different from those of precision andexplicitness, theoretical linguistics suffers from too much formalization atthe expense of proper focus on substantive matters concerning linguisticphenomena. The issues of concern can be reformulated this way. If rules ofgrammar covering syntax, semantics, morphology and phonology can be formulatedin a linguistic formalism-independent manner (without any fight over whetherrepresentational or derivational systems are true to linguistic phenomena),this strongly suggests that the faculty of language- whatever it actuallyturns out to be- is blind to formalism-internal issues (the debate overrepresentational versus derivational systems is just one example). This doesnot necessarily entail jettisoning any concern with the architecture of thefaculty of language. Rather, this paper aims to strongly argue that it neednot be the case. Operations in a general architecture of language can be quitefaithfully and transparently translated into axioms, rules and constraints ofgrammar/language, and this general architecture of language is general enoughto cover both the generality and idiosyncrasies of linguistic phenomenawithout having any inherently rigid configuration, which is what conferselasticity upon it. This is what ensures that the shift, however configured, canbe best realized to move over, from a preoccupation with universal/language-specific rule systems, to how rules of grammar covering syntax, semantics,morphology and phonology fit the specifications of the form and operations ofthe general architecture of language. So cases of grammaticality andungrammaticality/unacceptability will be equally covered under a well-conceptualized fit between rules of grammar covering syntax, semantics,morphology and phonology, and the specifications of the form and operations ofthe general architecture of language. This also helps not merely reconcile butalso intertwine axioms, rules and constraints as part of the linguistic systemwith pragmatic reasoning.

In the current framework, translational transparency is what provides us witha handle on the problem on substantive adequacy versus formal explicitness. Ifproblems of language acquisition and language description can be handled andalso explained in a manner that is consistent with the axioms, rules andconstraints within a general architecture of language, matters having to dowith the generative capacity can be reasonably separated from concerns having

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to do with language acquisition and language description. We will pursue thisline of reasoning in the next section.

6.Learnability, (computational) models of languageprocessing and the representation of the system ofrules, constraints and axioms

If the earlier discussion on the implications for linguistic theorystraightforwardly points to the importance of substantive adequacy, thisraises rather than strictly responds to questions of learnability when placedin the context of (computational) models of language processing. Form andmeaning-Saussure’s signifier and signified- can in fact be correlated with oneanother in innumerable possible ways with different grains of correspondencebetween form and meaning. This is what has been crucial in linguistic theoryand elsewhere with some approaches positing a closer coupling between them (asin Montague semantics) and some other a looser one (as in Generative Grammar).This issue is more crucial in the current context in that linguistic form doesnot have any atomic conception here by virtue of the fact that linguistic formis distributed across domains/components of grammar, that is, syntax, lexicon,phonology and morphology. Hence linguistic form is not any sort of monolithicentity; it has got its own complexities, idiosyncrasies and nuances in diversesets of manifestations as evident in cross-linguistic mismatches of form andmeaning. Meaning has, on the other hand, been restricted to the domain ofsemantics. This is necessitated by the observation that whatever islinguistically conceptualized can certainly be represented at differentlevels- lexical, phrasal and sentential (or even discoursal), but thedifferences between such levels of meaning- however represented-are not asontologically marked as they are in a situation in which syntax is contrastedwith phonology (syntactic rules cannot be reduced to phonological rules andvice versa) or phonology is contrasted with morphology (phonological rulescannot be reduced to morphological rules and vice versa). So in the presentcontext we have multiple possibilities of mapping between different types oflinguistic form (namely, syntax, lexicon, phonology and morphology) andmeaning (that is, the domain of semantics). This may raise a learnabilityproblem given that the space of all such possibilities of mapping betweentypes of linguistic form and meaning may well be computationally intractablegiven limitations on resources and the impossibility of defining computablefunctions on some mappings. Under this scenario, the constraints on theinteraction among the domains of language Ф= C1 …Cn come to the rescue as

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they reduce a lot of possibilities of mapping between different types oflinguistic form and meaning. Here we may conceive of this space as a hypothesisspace which is a subset of the space of all possibilities of mapping betweendifferent types of linguistic form and meaning that can be called the mappingspace. Now from a learnability-theoretic perspective, the important point isthat a hypothesis space may not always coincide with the learnable class oflanguages (Clark and Lappin 2011); thus it seems more appropriate to say thatthe learnable class of languages in the current context may but need not becharacterized to coincide with the hypothesis space that obtains with theapplication of constraints to possible mappings between different types oflinguistic form and meaning. Therefore, the learnable class of languages inthe current context may vary depending on what kind of constraints is imposedon what principles or procedures or systems concerned. For example, in theGold (1967) framework of learnability significant restrictions are put on theinference procedure so that an algorithm can converge on the target grammarupon the text presentation of the language data from which the inferenceprocedure can make out whether a word belongs to the target language (or theclass of learnable languages) or not. Similarly, restrictions can also comefrom the linguistic data on which a probability measure is imposed such that ameasure of the distance between the target grammar and the hypothesizedgrammar may not always be equal to 0. Real computational constraints onresources like memory-human or otherwise- and on time may also affect thecharacterization of the learnable class of languages. So do theoreticalassumptions regarding the nature of learners or learning including(over/under)generalization, postulation of multiple grammars by learners etc.

In the current context, it may be stated that such restrictions may also comefrom the source from which an inference procedure makes out data to operateon. So in any text presentation (which by its very nature does not contain anynegative evidence) in any natural language learning scenario that may notinvolve the presentation of negative evidence, both positive evidence andnegative evidence may come from different possible mappings between differenttypes of linguistic form and meaning given Ф= C1 …Cn and further globalmodulation by constraints of linguistic function, representation andprocessing. It is the splitting of linguistic form among different domains oflanguage and variable mappings of types of linguistic form onto meaning givenФ= C1 …Cn that can change the exact type of the learnable class of languagesin the current context. For instance, a language like Chinese barely has anymorphology; in such a case the text presentation may not include any relevantinformation about morphological cues including agreement etc. which are

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significant for the learning of the grammar of Chinese. In the currentframework, such cues may well come from other types of linguistic form likephonology and/or from relevant mappings of types of linguistic form ontomeaning constituting a constrained space out of the overall hypothesis space.And this may change the class of learnable languages since the type oflearnable grammar type may be context-free grammars or context-sensitivegrammars depending on the restrictions arising out of possible mappingsbetween different types of linguistic form and meaning given Ф= C1 …Cn eventhough the hypothesis space may well define recursive sets or recursivelyenumerable sets. This is not surprising given that the conditions under whicha certain class of learnable languages qualifies as learnable vary withcertain definitional assumptions and other restrictions (Savitch 1987). Onlyunder such characterization does this matter relate in a reasonable manner to(computational) models of language processing, for a (computational) model oflanguage processing has to meet the demands of both cognitive plausibility andfaithfulness to linguistic rules and constraints however construed. At thesame time, it also holds true that certain assumptions- however explicit orimplicit- about (computational) models of language processing underlie theformulation of learnability in computational learning theory when applied tonatural language. In such a scenario, if it turns out, on one hand, thatproperties of representation of the grammar type which qualifies as learnablematter to a conception of learnability and on the other hand, that operationsin a general architecture of language can be quite faithfully andtransparently translated into axioms, rules and constraints ofgrammar/language, the formulation of learnability as it applies in naturallanguage acquisition/learning can be made either at the level of the generalarchitecture of language or at the representational level of axioms, rules andconstraints of grammar/language as specified here, with a transparent shiftbetween the two levels as and when required.

Now this has consequences for (computational) models of language processing.The formulation of learnability relevant to natural languageacquisition/learning can thus exploit features and properties of therepresentational level of axioms, rules and constraints of grammar/languagewhen we go about specifying the grammar type that qualifies as learnable, aswell as aspects of the level of the general architecture of language whenoperations of the general architecture of language in its cognitive nicheconfigure the learning setting (involving inferences driven by processingconsiderations as in garden-path sentences, influence of linguistic functionas in semantic-pragmatic grounding, representational constraints on mental

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structures as in the specification of linguistic representations in terms offinite-state automata etc.). Ultimately, a computational model-whether aprobabilistic model of symbolic rules and representations or a connectionistmodel grounded in neural networks- has to learn as well on the basis of inputdata only to approximate or converge on the target grammar type. If so, itappears that computational models of language processing may also bepositioned, by virtue of an intrinsic link to learnability considerations, ontranslational transparency between operations in a general architecture oflanguage and a system of axioms, rules and constraints of grammar/language.But this is not quite right because such computational models cannotthemselves be identified with any part of the general architecture of languagein Figure 1 and thus do not on their own inherit translational transparencybetween operations in a general architecture of language and a system ofaxioms, rules and constraints of grammar/language. Had this been true, suchcomputational models of language processing would not in the first place havebeen models that (try to) encode and instantiate the form of the exact tokensor types of rules and constraints in specific languages. Whereas in thepresent context translational transparency between operations in a generalarchitecture of language and a system of axioms, rules and constraints ofgrammar/language does not in fact suggest that the general architecture oflanguage in Figure 1 instantiates or individuates rules, axioms or constraintsin an explicit sense (as in a calculator that explicitly encodes rules ofaddition, multiplication and division) (see for details, Pylyshyn 1991).Certainly, the general architecture of language in Figure 1 does notexplicitly encode the system of axioms, rules and constraints ofgrammar/language as specified above; but it seems that it does that in animplicit sense (as reflected, for instance, in the visual system throughassumptions that involve light reflection from the surface, mapping ofphysical discontinuities onto the visual images etc.) in the sense thatinterpretations of the operations of the general architecture of language mustbe compatible with the system of axioms, rules and constraints ofgrammar/language implicit in the structure of the general architecture oflanguage. However, there is more to it than meets the eye. There is still someresidue left which is not captured by this implicit sense as well. Forexample, when water transforms into ice or vice versa, it can be said thatwater and ice are two different states of the same molecules in H2O underdifferent external conditions and are thus latent or implicit in each other.But we cannot say that water conforms to the structural constraints of ice orvice versa any more than we can say that a group of certain constraints(implicitly) assumed in the visual system and the visual system are different

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states of the same thing. So in the present context translational transparencybetween operations in a general architecture of language and a system ofaxioms, rules and constraints of grammar/language means, more than anythingelse, that the two are different descriptions of the same system underdifferent logical/conceptual conditions.

7.Concluding remarksThis paper has tried to show how three goals having to do with linguisticrules and the operations of the postulated general architecture of the facultyof language can be achieved so as to help us demarcate the issues of concernin linguistic theory. Implications for linguistic theory as ensuing from thishave been drawn up to show a viability of the program thus construed. Withinthe space of the current paper, it has not certainly been possible to dojustice to all the pertinent issues and details. Further research can perhapsilluminate these matters with a greater focus and precision.

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