Segal Logical Concepts

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Psy 416: Reasoning and Problem SolvingPrimer on Logic and Logical Concepts

Erwin M. Segalepartment o! Psyc"ology and

Center !or Cognitive ScienceState #niversity o! $ew %or& at '(!!alo

Logic was an attempt to describe normativeor correct reasoning. A widespread belief in AI,Cognitive Psychology, and Cognitive Science is that there are procedures representing the way

people think which can be implemented on computers using logic type rules directly algorithms!

or by finding other ways to implement logical principles. "he study of reasoning in this case is

the study of #natural# logic. $uch reasoning is evaluated by the e%tent to which it conforms tological analyses, and much reasoning research in psychology is aimed at e%plaining the errors

people make when they attempt to solve logic type problems.

Logical reasoning focuses on one aspect of how human cognitive performance can be &udged. 'o

the statements that are presented together in a single discourse hold together( Are the statementsconsistent with one another) and if any conclusions are drawn, do they legitimately follow from

the other statements made( Are they logical or are they illogical( *e hope to clarify what theseterms and other terms mean, and give at least some simple e%amples of how to answer such

+uestions. Logical analysis is based on the structuralor the formalrelations among the

components of the arguments rather than the meanings of the components. If two arguments havethe same logical formone cannot be logical and the other not, regardless of their differences in

meaning.

"here are many different logics with many similarities and some differences. Logics are formal

systems that include principles which identify wellformed formulas, a set of a%ioms, and rulesof derivation, which when correctly applied purportedly lead to correct conclusions. 'ifferent

logics may reason about categories, propositions, relations, time, tenses, beliefs, necessity,events, etc.

I. General concepts:

DeductionApplying a se+uence of rules of inference from a set of premises and from which

a conclusion necessarily follows.

Inductioncoming to a conclusion that is likely from the premises. -sually coming to a

conclusion about a universal or a particular from previous instances of particulars.

Proposition A concept that usually represents a statement, a sentence, or an assertion. /.g.

The moon is made of green cheese. 010 2 3.Five is greater than seven.'r. Segal teaches Psy345.All men are mortal.It6s better to have loved and lost than never to have loved at all.

Sammy Sosa didnt hit any homeruns yesterday. 7edipus loved his mother! Sentences which

represent propositions in most logics, should have a truth value) $any logics are called two-

value logics, in that they assume that all propositions are either true or false. In formal logic

different kinds of propositions are represented by wellspecified structures or forms. In any

formal logical system a given representation of form for! a proposition should be clear andunambiguous. Such forms are often called well-formed formulasor wffs.

Premise A proposition that is assumed to be true for the sake of a logical argument.

Argument A se+uence of propositions, starting with premises, which purportedly &ustifies

another proposition, called a conclusion.


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Syllogism:A set of usually, but not necessarily, two! premises followed by a conclusion) the

classical form of an argument.

Validity: A syllogism or any argument is validif the conclusions! drawn logically followfrom the premises) otherwise it is invalid. In a valid argument if the premises are true, the

conclusion is necessarily true.

Soundness:A soundargument is a valid argument in which the premises are true.

Primer on Logic/. $. Segal

II. !ategorical "ogic:

!ategorical propositions Propositions of a sub&ectpredicate type connected by a copula

is, are!. "he sub&ect is an individuale.g. Socrates, 8ohn, this book! or a categoryeg. men,elephants, green things!, and the predicate is a category. Propositions define a relationship

between the sub&ect and predicate.

"ypes of categorical propositions Aristotelian!a! -niversal affirmative, e.g. All men are mortal) All water is wet!

b! -niversal negative, e.g. 9o men are mortal) 9o apple is sweet!

c! Particular affirmative, e.g. Some men are mortal) Some paperclips are plastic!, and

d! Particular negative, e.g. Some men are not mortal) Some talk show hosts are notracists!

In studying Categorical Logic, one can substitute varia#lese.g. A, :, S, P! for the

categories.

In a syllogism the two premises each contain a common category the middle term! and a

uni+ue one. "he conclusion contains the uni+ue categories from the premises. e.g., Some A

are :, 9o : are C, "herefore 9o A are C!. Some syllogisms are valid and some such as this

e%ample! are invalid.Syllogisms

III. $elational terms and linear reasoning.

$elations:"here are relations in addition to a copula. Aristotle did notconsider these in hiscategorical! logic. 7ne can specify various relations between the sub&ect and predicate terms

e.g. greater than, e+ual to, not e+ual to, hit!. "he relationship has content) different relations

imply different logical properties.

Linear Problems

If a relation is between two ob&ects, it is called a #inaryrelation, and the ob&ects are referred

to as arguments of the relation. In the propositionA is greater than B, ;ormally this can bewritten a


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Intransitivee.g. ne%t to, sees! a?b and b?c does not imply a?c.

Symmetricale.g. similar to, near, e+ual to, not e+ual to!, def.! If a?b, then b?a.

$efle'ivee.g. identical to, e+ual to! def.! a?a.

IV. !onditional $easoning and Sym#olic "ogic.

Symbolic logic refers to formal reasoning systems.

?easoning principles are rules of inference based on the form of the representations.(ell-formed formulas:A notational system will define symbol strings that represent

propositions. 7ther strings cannot formally represent propositions.

In )lementary propositional or sentential logic

Simple propositions are not formally analy@ed. "hey are often represented by a single letter,

e.g., A, :!. Compound propositions are formed by combining simple propositions using

#logical terms# to connect propositions with one another.

"ogical termsinclude not, which relates to a single proposition e.g., A. If A is The sky isblue, A not A! is!t is not the case that the sky is blue, or The sky is not blue!. Some other

logical connectives are and, or, if then, and if and only if. "hese relate two propositions

e.g., AB:, A:, A:, A:, readA and B,A or B, !f A then B, andA if and only if B,

respectively.In many logics these connectives are truth functional) that is, they assign truth values to the

compound propositions only as a function of the truth values of the simpler propositions theycontain.

"aw of the e'cluded middleAll propositions are either true or false. "his means we must

assign a truth value to any sentence if we are to analy@e an argument using this logic. $ostif not all! logics of this type obey this law.

%ruth functional logic"ruth of composite propositions is determined by the truth of its

component propositions

?ules of inference Principles by which one can verify the validity of conclusions from

premises. Some rules of inference in propositional logic include *odus PonensIf A:,

and A, conclude :!, *odus %ollensIf A:, and :, conclude A!.+ypothetical Syllogism

If A:, and :C, conclude AC!

%autology a logically true sentenceA sentence which has to be true by form alone, i.e.whatever the truth of its component propositions, it is true. /.g. The "ankees #ill either #in

the $orld Series this year or they #ill not #in the $orld Series this year.

)mpirical sentenceA sentence representing a proposition that may be true or false. /.g. !tis raining in Bei%ing.

"ogically false sentenceA sentence that must be false as determined by its form alone.

/.g.!t is raining and it is not raining in Bei%ing. Joe gave &'( of the )ie he baked to each of

three friends. is a false sentence and is necessarily false, but its falseness depends on the

meanings of the terms DE and three, not on the sentence form, therefore it is not falsebecause of its form.!

%ruth ta#leF "he truth of the composite propositions in certain logics are determinedentirely by the truth of its component propositions. A way to represent truth of composite

propositions as a function of the truth of its component propositions. "hese may represent

whether a composite proposition is a tautology, an empirical sentence, or a logically falseone. "ruth tables may also be used to evaluate whether an argument is valid or not.


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In a truth table the top row contains the elementary propositions and the set of composite

propositions that comprise the proposition under analysis. ;or each of the remaining rows of

the table the truth of the elementary propositions are assigned systematically such that eachrow has a different combination of truth values. "he truth of the composite propositions are

then determined by the rules of assignment, that is what their truth value would be if the

elementary propositions had the truth of their assignment for that row. 7ne might envision agiven row as a possible world where the truths af the elementary propositions are as assigned.

In that world, in a truth functional logic, each composite proposition has the truth of its rule

governed assignment. Some elementary e%amples P, G, and ? stand for elementary

propositions) means 6not6) B means 6and,6 means 6or,6 means 6ifHthenH6, and means

6if and only if6. In the tables " is the semantic assignment of 6true6 and ; the assignment of

6false.6

"able 4

P P

" ;

; "

"able 4 asserts if P is true, not P is false row 4!) and if P is false, not P is true row 0!.

"able 0

P G PBG PG P G PG

" " " " " "

" ; ; " ; ;

; " ; " " ;

; ; ; ; " "

"able 0 represents several of the logical connectives. In it you can see that according to thissimple logic

a. PBG is true if P is true and G is true, and is false otherwise ;rom columns 4, 0, and

!.b. PG is true if P is true, if G is true, or if both P and G are true. It is false only when

both arguments, P and G are false.

c. P G is false only when P is true and G is false. It is true whenever P is false. "hese

latter cases are called #counterfactual conditionals and are the basis for much discussion

and controversy.

d. PG is true if the truth values of P and G are the same and false if they are different.

Primer on Logic

Page

/. $. Segal

V. Predicate logics ,predicate calculus

Logics which represent individuals, and predicates and relations. -sually they also contain

variables and +uantifiers.

Argument Second concept called argument the first being a set of premises leading to a

conclusion!. "his refers to a component of a proposition or sentence in a predicate logic.


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It represents an individual thing. It is something like a noun or a pronoun. Arguments

tend to be represented by lower case letters in formal logics.

Predicate something like a verb or an ad&ective. It often represents a property, relation oraction. *hen a predicate is combined with the correct number of arguments it is a simple

sentence or proposition. 7ften a predicate is represented symbolically by a capital letter.

A given predicate must have a predetermined number of arguments associated with it. eg.4! ?ed, tall, smart are one argument predicates. #"b# might mean #"he boy is tall# or

#"he tall boy# 0! larger than, hit, kissed, are two argument predicates Jbg might mean

#"he boy kissed the girl.# In multiple argument predicates, the order of the argumentsdetermines their role in the predicate relation. Lab might mean #A is larger than :.# It

could not also mean #: is larger than A.# ! there are a few three and four place

predicates as well, e.g. give, put. #8ohn gave the book to $ary.#

uantifiersand varia#les

7ne might say something like #Some people are tall.# "his might be represented as %!

P%B"%!. %!, the e'istential operator means that something represented by the

variable % e%ists. :y itself it is an incomplete e%pression. P% and "%, which are said to be

in the scope of the +uantifier, say 6% is P6 % is a person!, and 6% is "6 % is tall!. 9either P%nor "% are complete propositions because without being +uantified they have no truth

value. "ou cannot decide #hether * is a )erson until you kno# #hat * refers to. Kowever

#"here e%ists an % such that % is a person# is true if at least one person e%ists. #"heree%ists an % such that % is a person and % is tall# is true if there is at least one tall person.

"hus the +uantified e%pression is a proposition.

"he sentence #All men are mortal# is represented using the universal operator)! or

often %!. Logicians identified this proposition as a conditional %!$an% $ortal% !. "his

is usually e%pressed as #;or all %, if % is a man then % is mortal.#"he two propositional representations of the sentences #Some people are tall# and #All

men are mortal# may not look like the /nglish sentences, but if you think about it you

may see that they would be true in e%actly the same circumstances, thus the /nglishsentences and the formal notation represent the same propositions.

;or your information, there are other logics, some called modal logics, have usually beenabout necessity and possibility) but may be about time or space or beliefs, etc. "hese

logics often are not strictly truth functional. "hat is the truth of a whole proposition may

not be simple function of the truth of its parts. "hink about this If a proposition ispossible it may either be true or falseJohn is tall. If it is necessary, it must be true+ither

S)ot is a dog or S)ot is not a dog. If it is not possible, it must be false, The cat is both

alive and not alive. And if it is not necessary, it may be true or false) Sosa #ill hit '

homeruns in -'''. ;ormal Logic re+uires a formal representational system, a set of

a%ioms, and rules of derivation. It does not re+uire strict truth functionality.VI. "ogical derivation.

A widespread AI, Cognitive Psychology, and Cognitive Science principle is that there are

procedures which can be implemented on computers which represent the way that people

think. "hese involve applying logic type rules to a formal representation base. "hepsychological study of reasoning in this case is the discovery of the form of the

representation and the rules of inference that people use when they reason.


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a.Incoming information is transformed into a symbolic representation of the

implied proposition. "here are certain formal ways in which propositions are

interrelated and conclusions are derived. "hese are implemented by theapplication of logiclike rules. In information processing systems they are the

application of efficient procedures which represent algorithms or heuristics.

#.Logic and other! problems are solved by the use of formally valid derivationson symbolic representations) apply logical rules directly to 6sentences6 which

represent propositions. ?ules of inference include such as modus ponens, modus

tollens, and hypothetical syllogism.

c. /rrors occur when a! there is an error in the representation, b! the derivation is

not completed, or c! the problem solver applies the wrong rule.

A problem of application is it is not always clear how to get from premises torepresentations, nor for some problems what the derivation rules are. "he basic

ideas for applying rules ties this process into some of those in computation. "hree

relevant concepts are

)ffective procedurea procedure which transforms a form e.g. proposition! into

another one in a well specified way. "he concept of 6effective procedure6 is one of

the more important concepts in the symbolic sciences, and one which is needed atleast on an informal basis in order to work within any cognitive science. #An

effective procedure is a finite, unambiguous description of a finite set of

operations. "he operations must be effective in the sense that there is a strictlymechanical procedure for completing them#

Algorithma se+uence of effective procedures that is guaranteed to solve a

problem. or produce a valid outcome.

+euristican effective procedure that is likely to solve a problem relatively+uickly.

"here are times when the goal of identifying an effective procedure is not reached butthe term heuristic is still applied. Keuristics are often called 6rules of thumb.6

VII. (ason/s Selection tas0

4. If a card has a vowel on one side, it has an even number on the other /, J, 3, MNO

"ry to set this up according to formal rules of symbolic logic.

7ther versions

0. /very time I go to $anchester, I go by car $anchester, Leeds, Car, "rainN

. If the envelope is sealed it needs a c stamp. c, c, sealed, unsealedN

3. If someone is drinking beer, she must be over 04 beer, coke, 0, 4MN

. /very time I eat haddock, I drink gin haddock, cod, gin, scotchN

5. If a student is to be assigned to


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Causal relations and mechanisms, e%pectancies,

Permission view. 'eontic reasoning moral obligation, what one ought to do.

OIn order, the cards represent P, P, G, GN

Psy 416: Reasoning and Problem SolvingDeduction: Form, logic, and logical reasoning

Erwin Segal

1. "ogical appraisal

*hen a person says or writes something there are many different ways in which her performance

may be &udged. 'id she say something nice( 'id she speak well( 'id she articulate clearly(

Could I understand what she meant to say( Kas she used apt metaphors( *e may take anynumber of different stances to her discourse. Among these is a logical stance. In this stance

arguments are evaluated for their truth and validity.

*e may e%amine the logical structure of a discourse and evaluate whether it can withstandlogical analysis. *e can evaluate to what e%tent the conclusions drawn are &ustified by the

premises.

Logic is reasoning based on the idea that often ifsome statement or set of statements is true,some other possible statements mustalso be true, others may be true and may be false, and still

others must be false. *e all probably reason this way some of the time.

;or e%ample, if you knew the following two statements to be true

4a! If a person does not practice, he or she will not become an accomplished pianist.

4b! Susan took piano lessons for years, but she never practiced.

you could conclude

4c! Susan is not an accomplished pianist.


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IV. An alternative approach is based on implementing the premises in models. $odels come in

different variants, lists of tokens, Qenn diagrams, images of the details of the propositions

described. etc. e.g. 8ohnsonLaird, 4R, $ental $odels, Karvard -niv. Press!

4. $odel building is one way that people tend to solve logic! problems

a! they attempt to build a mental or e%ternal! structural representation 2model! of

the relevant content information in the premises,b! then interrogate the model to see whether the conclusion is already contained

there.

c! if so, conclude that the argument is valid) if not conclude that it is invalid.0. ?easoning may fail when

a! model does not accurately reflect premises

b! model only incompletely represents premises

b! models of premises are not integrated accuratelye.g. representation of earlierpremises may not be incorporated when later premises are added

c! if person is using mental models, model of premises is not remembered during

conclusion evaluation

d! interrogation is not accurately completed.. Problems with model theories

a! "here is no single universal structure for mental models of propositions.

b! It is not always clear what the relevant components are.

c! It is not obvious how to model some meanings) some meanings are very difficult

to model using certain model schemata.

d! It is not always clear how people may interrogate the model, nor is it always clear

how to use the model to draw valid conclusions.

IV. Although much psychological research has been done on reasoning based on logical form,

logical reasoning seems to be secondary to reasoning from content in many instances. Contentreasoning may be based on previous knowledge or even innate tendencies to use certain

reasoning schemas.

Psy 416: Reasoning and Problem SolvingIntroduction

I. %he course has three #asic components.

4. %heoretical and +istorical 2verview of different approaches to the ac+uisition ofknowledge and skilled performance, and the kinds of evidence brought in support of

those approaches.

0. Analytic approaches:*hat are some concepts and mechanisms that have the possibilityof accounting for valid reasoning, effective problem solving, &ustified decisions and

skilled performance( Kere we are going to learn some fairly specific principles that many

cognitive scientists believe underlie these activities.

. )mpirical studies of reasoning pro#lem solving and other comple' acts: *hat dowe do( *hy do we do it( And what insights may allow some of us to do it better(! Kow

do we achieve the competence to do these things(

II. 3rief Glossary

Pro#lemsare situations givens! in which one has a goal he or she wishes to achieve. 7ften,

and sometimes re+uired for the situation to be considered a realproblem the way to achieve

that goal is not obvious obstacles!.

Pro#lem solvingis the process by which a goal is achieved.


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$easoningis the study of a set of problems with certain moreorless! welldefined

constraints and symbolic solutions.

"ogicis the study of formal rules which purportedly underlie correct reasoning.

Decision *a0ingis the selection of one option from a set of possibilities.

)'pertiseis a state of skill or competence that a person may reach after training or

e%perience. 7ne can envision a continuum from being a novice to being an e%pert. !reativity is a skill or talent that some people seem to have in producing novel and

interesting products or solutions to problems.

Intelligencecan be associated with positive cognitive activity or behavior. 7ne manifestsintelligence by reasoning well, solving problems easily, acting rationally, learning comple%

material +uickly, etc. $any think of intelligence as a special measurable property on which

people vary.

III. A pro#lem approach

1. (illiam 4ames on functional definition of mind.

$ind is displayed when the path varies and the goal remains the same.

5. A Structural view of pro#lems: Components in 9ewell and Simon6s #statespace#

analysis$ayer p !

a. Problem space.

b. initial state

c. intermediate statesd. goal statee. moves, transformations, or operations

*elldefined and illdefined problems.

IV. %ypology and dimensionality of pro#lems

a. 7perations on symbolsIndividual


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Controlled association!

. Perceptual problems *here6s *aldo, ;ind words in letter matri%, ;ind animals in picture,

reading an %ray!

4D. Playing games well Chess, poker, bridge, consider particular moves in a game!!

44. Creating novel ob&ects *riting an essay, composing a sonata, painting a picture, carving

a statue,inventing a device, proposing a new scientific theory40. /valuating a claim scientific theories, charges of a crime, designing e%periments, ,

4. Skilled performance problems a! individualPlaying golf correcting a slice!, playing a

sonata, painting a picture, carving a statue, removing a brain tumor, shooting a basketball) b!competitiveplaying tennis, football, basketball) c! cooperativesinging in a chorus, playing

in an orchestra

43. $emory search Answering +uestions, "aking a test, recalling a phone number,

4. Passing a test,


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Associationism including atomism, mechanism, and empiricism is still with us. $odern

neuroscience and cognitive approaches to problem solving have created very popular new

approaches using associationistic principles, especially in connectionist, P'P, or neural nettheory.

Some more "istorical #ers#ectives

!ommon Sense ca 4MD! *e have built in faculties of mind which provide the answerF?eid.Kow do I know that a rose is #out there# instead of in my head( ;aculty psychology dominated

psychology and education until the 0Dth Century.

(undt: ca 4RRD!.Comple% mental processes must be studied through the artifacts of humansand cannot be studied directly by e%periment. /%perimentally one can only study components of

sensation.Artifacts are the products of human activities :ooks, paintings, houses, computers,

cities, governments, languages, domesticated animals, armies, telephone systems, universities,

footballs, football games, football leagues.

67lpe and the (7r8#urg School: ca 44D! /%perimented on comple% mental processes and

concluded that reasoning re+uires concepts such as directed thought and unconscious processes.

JUlpe gave sub&ects problems to solve, answers were analy@ed and ?eaction "imes ?"! were

measured. Sometimes the process was interrupted and sub&ects described what they werethinking or imaging.

99Gestalt and +olism: ca 440!. /%periments in perception and problem solving. Concludedthat thinking is a holistic process based on the gestalt or form of the phenomena to be reasoned

about. /lements are defined in relation to their conte%t rather than the other way around.

?easoning processes include, re!organi@ation, insight, autonomous processes.

Information Processing: ca 45D!Fcomputation, input, transformation, storage, and output of

information. Information processing analyses have become the core of Cognitive Psychology and

much of the content in this course is at least partially dependent upon this approach. Almost

everyone in the field, classical rationalists, evolutionary nativists, modern behaviorists,connectionists, and


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5. Gestalt Psychologists:

emphasi@ed demonstrations and creative solutions to problems, rather than

performance improvement

looked for new relations among parts, or between parts and wholes, not inputoutput

connections

claimed that transfer is based on identifying similar structures, not identical

connections.

had a primary goal of understanding. "here is a search for meaningful simple,

straightforward! structural fits of the components to one another and the whole.

were critical of blind habitual responses rote learning!, or #stupid# application of

rules should understand why they work!

thought a problem solver needs to #see# the problem as a whole

believed insight and restructuring important to real problem solving

felt the role of past e%perience is problematic


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in its emphasis on the difference between ha@y concepts, ha@y generali@ations, and

e%act formulations)

in the development of a host of formal criteria which are suited for testing for, and

discovering mistakes, ha@iness in thinking, such as un&ustified generali@ation,

&umping at conclusions)

in its emphasis on proof)

in the seriousness of the rules of discussion)

in the insistence on stringency and rigor in each individual step in thinking.#

=. "he crucial issue in each of these problems, from the


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0. ;or the behaviorists the elements were primarily stimuli and responses. In the study of memory by /bbinghaus and others the elements were often words.

3. Images, feelings, stimuli, behaviors, secretions, implicit behavior, neuronal activity.

. $odern connectionists identify distributed sets of units that collectively represent stimuli,

responses, or internal states.


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;. !onnectionist models: A modern associationist view of cognition

*ith modern advances of the understanding of the central nervous system, particularly the fact

that most neurons in the Central 9ervous System have thousands of synaptic connections, a newbreed of computational approach to psychology has developed.9otes on Connectionism.If you

are interested in learning more about the nervous system, I have notes with links to *eb

information available from my Cognitive Psychology course of last year.>. $esidual issues in Association %heory

4. "ransfer of training

0. $ediation theoryse+uences of elements, many of them hidden

. Connectionist theoriescurrently some of the most popular theories in psychology

3. 9eural locali@ation of function

?. An Alternative view of the Anagram %as0

%as0 analysis

Structure *ords, syllables, consonant clusters, fre+uency, target areas

Strategies.

4. Count vowels and consonants,

0. "ry for high fre+uency groupings in the right place in a word

. Search for words with same letters as presented string

3. Search within a category

Psy 416: Reasoning and Problem Solving &once#t 'earning and Induction

/rwin Segal1. Induction and deduction%wo 0inds of 0nowledge ,B empirical and analytical

a. Induction: Cncertain Generali8ations from e'perience Predictions of future

e'perience. Induction is generally a#out trying to ma0e sense out of data.

2ften thought of as going from specific to general or specific to specific.

b. Deduction: !ertain !onclusions from premises "ogical conseuences of

arguments mathematical derivations. 2ften thought of as going from

general statements to the specific events or statements or from general

statements to general statements.

5. !oncepts or categories: *uch of the research on induction presumes the concept of

Econcept.E

a. A concept is usually #ut not always identified #y a noun or noun phrasewhich is often thought to #e defina#le #y a set of properties.

b. Properties ,red large circle alive animal are often operationali8ed as

values of dimensions such as color si8e num#er etc.

c. Some concepts may #e simple such as /red things/F some may consist of a

conunction of properties such as /two red circles./ Sometimes a concept may

#e defined EdisunctivelyE such as a stri0e in #ase#all. Sometimes it/s hard to
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identify the dimension to which a property #elongs or to identify the set of

necessary and sufficient features that identify a concept.

d. Sometimes the #est we can do is to identify whether an e'ample is an

e'emplar of a concept pro#a#alistically.

e. Sometimes we may not #e a#le to identify the dimensions or the features that

define a concept with accuracy.


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discontinuityBImplicit and e'plicit processesBAutomatic and deli#erative

,conscious processesB

;. 4udgment and Decision %heory: (hat is involved in ma0ing a decision in order to actB

Since one often solves problems and reasons in order to take some action or to come to some

decision, 'ecision "heory is closely tied to many topics in this course. 7ur te%tbook approaches

it as a set of problems in induction. Kastie 0DD4! outlines the nature of the topic. "versky andJahneman have made ma&or contributions to its psychological understanding. >. 4udgmentunder uncertainty: 6ahneman and %vers0yuse of heuristics and their limitations.

a. Availa#ility: %hin0 of e'amples

b. $epresentativeness: +ow do properties fit those of category prototypeB

c. $ole of #ase ratesB

Psy 416: Reasoning and Problem Solving..345STLfD4.htm

In(ormation #rocessing and com#uter simulationSo(rces on some o! t"ese iss(es are accessible !rom t"e re!erences

/. Segal

People function in the world. In order to do so, we must gain knowledge about things and eventsand be able to act in the world. $uch of the time we act appropriately to the people, ob&ects, andevents we encounter. A ma&or +uestion for Cognitive Psychologists is Kow do we function so

well(

7ne general answer, one that has incredible power, is that humans and many other organisms, are

Information Processing Systems. $any, but not all, of our interactions with the world is viainformation.

Information Processing IP! is the dominant perspective held by cognitive psychologists and

many others in the Information Sciences! for the last D years or so. "his perspective holds thatcognition meansthe input, storage, transduction and transmission of information, and that the

problems that cognitive psychologists face are all connected to Information Processing.

Guestions asked by Information Processing Psychologists almost all relate to Information *hatinformation do we respond to( Kow is it stored( *hat are its properties( Kow is it accessed(

Kow is it transduced( *hat conditions enhance IP( Kow is it used( Kow is information

represented in the organism( etc.

1) *"at is In(ormation+Qery few Information Processing sources actually define their core concept. Some researchers

use the term informally and its meaning varies from one use to another. I find that many who use

the term are not clear about what it means. I think that Information is probably best defined as a

patternthat #rides# on matter or energy. Information has the property that the same pattern can

ride on different kinds of matter or energy. In information sciences, patterns and structures are

the primary focus of study. 9orbert *iener, an early champion of cy#ernetics, argued that the

concept of information changed the view of causality in science. 7ne entity can cause a changein another with only an infinitesimal transference of energy. "he causer or controller does it with

a signal rather than a push.

Information is a key to understanding much of the modern world including communication and

computation. $odern technological devices from telephones, radios, computers, and the internet

have developed in great part because of informational analysis.

Although any pattern that rides on matter or energy may be considered information, for manymodern analyses, the patterns are set up to be, or analy@ed as, concatenations of symbols. ;or
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e%ample, this page consists of information represented by the concatenation of letters to form

/nglish words, sentences, and paragraphs. *hen the symbol system being contains a small finite

number of symbols which are concatenated to make larger structures, the system is a discreteor

digital one.

"he cognitive and informational sciences owe their very e%istence to the study of information

storage, transmission, and transduction. Tou have heard of flow charts. In psychology,communication and computer science, flow charts chart the flow of information. $ore on information

) In(ormation #rocessing systems: Simon and -ewellAn analysis follows what happens from the beginning of a task, such as being given a problem tosolve to the end with the problem solved. "he basic theory is that much of the se+uence of events

can be thought of as the movement, storage and transformation of information.

.a/or com#onents

receptorssenses

processorstransform, interpret, integrate, selectattention, set, automatic and controlled

processes.

memorieslong term, short term, working, S"SS.

effectorsmuscles, glands

Information enters the system via the receptors and then is transformed and operated on bythe processors, some intervening outputs are temporarily stored and others are more

permanently stored in memory, outputs are generated which lead to behavior and interaction

with the environment. Kistorically, information processing psychologists have used flowcharts to identify the path of the information through the cognitive processing system.

Let us attempt to concreti@e the idea of information and information processing. An IPS has

several components including receptors, memories, processors, and effectors 9ewell B

Simon, 4M0!. Such systems receive information from the environment through theirreceptors. "hey then go through processes of transforming, storing, comparing and

evaluating this information. ;or e%ample, assume that you see a duck. *hat happens

informationally( In order for you to know that you see a duck, or to be aware that it is a duckyou see, you have to compare part of the visual input with some representation of a duck in

memory. Processors must parse the visual stimulus into meaningful components in order to

isolate the duck from its visual conte%t, and to compare the resultant duck information to amemorial representation. "he representation must include not only information concerning

the visual appearance of a duck, but also information identifying the visual information to be

that of a duck. In order to behave

appropriately, therefore intelligently, such as to say #7h, there6s a duck.# there has to be a linkbetween your representation of the visual appearance and a representation of the verbal form

#duck.# In addition, this information has to tie to devices which control the effectors in your

vocal apparatus.

0) &om#utation t"eory"he concept of 6effective procedure6 is one of the more important concepts in the symbolic

sciences, and one which is needed at least on an informal basis in order to work within anycognitive science. #An effective procedureis a finite, unambiguous description of a finite set

of operations. "he operations must be effective in the sense that there is a strictly mechanical

procedure for completing them#

Algorithm An effective procedure which is guaranteed to solve a problem.

Cniversal %uring *achine An particular abstract information processing system
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consisting of a linear tape, a read head, and a finite set of states. It can read the tape for

either of two symbols, it can write either of the two symbols, it can move one unit to

either the left or right, and it can switch from one state to another. "hat is all. Correctlyprogrammed a "uring machine can solve any problem for which one can specify an

algorithm. "here are, however, unsolvable problems


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,e"he P$S level is the functional level at which intentions, plans, and purposes are

reali@ed. #Kere there is simply a medium, called data or information, which flows along

channels called links and switches and is held and processed by units called memories,processors, controls, and transducers.#

) $nalysis o( #roblem solving (rom an In(ormation Processing #ers#ective:

&ewell and Simon/s analysis1Identifying the problem space. "he first stage of an analysis of a problem is to identify

the initial and goal states 9ewell B Simon, 4M0!. "hese two states define the boundary

of the problem space. "he larger the #distance# between the two states the larger theproblem space.

5 Identifying some of the intermediate states between the initial and goal state. 7nly for

trivial problems can the solver go directly from the initial state to the goal state. "here are

usually going to be relatively stable describable intermediate states which need to bereached. :oth the problem solver and the analyst may need to know of these.


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basically a information processing computational! device. Information processing is a set of

se+uential or simultaneous processes, each of which take time to complete. If we can figure out

how much time different tasks take and the conse+uences of limiting available time, perhaps wecan get some insights into the algorithms used by the problem solver to solve the problems. In

addition creative e%perimentation gives tentative! answers to how some of these algorithms may

be implemented."he two primary methods of measuring how long processes take to complete are $eaction %ime

e'periments?"! and %achistoscopic e'posure time ,)%e%periments. :y measuring how

long it takes to do different tasks ?"!, or by measuring how good performance is for differenttasks after a limited amount of time to work on it /"!, a researcher can generate theories about

what underlying processes are involved. A large amount of cognitive research uses variants of

these methods.

'onders and the su#tractive method

4. Simple ?" ?"2to0.


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"he models are conceptually compatible with the general information processing models and

thus with computational models. 7ne can simulate these processes. Such modeling is one of the

ma&or pastimes of many AI researchers.;or tasks that re+uire fairly comple% processing steps,certain researchers have introduced a modification of old introspective reports. Sub&ects are

asked to 6think aloud6 while they are attempting to solve a problem. Sub&ects thus report their

e%perience, what they are attending to, and what their intentions are 6online6, that is, while theprocess is going on. "his generates a record of the se+uence of processes which can then be

analy@ed and converted into an effective procedure representing the heuristics used during the

problemsolving activity.

Reasoning and Problem Solving/rwin Segal

Semantic .emory"he basic idea behind Chapter is that each of us knows a lot. "his knowledge must be

represented in our minds somehow. It is probably organi@ed in some meaningful way. "here are

e%perimental methods by which we can gain insight into the structure of memory. ;or this class,

we can think of this as background information on how we may solve simple problems such as

answering +uestions based on this knowledge. Chapter M presents evidence that different mental tasks take time, and there are ways to try to

find an algorithm that can do the tasks. It6s implicit assumption is that each component of analgorithm takes time to perform. If the algorithm for "ask : has more se+uential components in

it than the one for "ask A) especially if the other components of the algorithm are the same, it

should take longer to do. Chapter adds to this analysis the idea that the information about theworld in our memories is structured in some meaningful way. ?easoning on this memory

depends on making e%plicit, relations among these components that are not directly e%pressed. It

takes time to operate on the relations that we have in order to generate the ones that we need."hese operations are often logical inferences based on the network of relations which are

e%plicitly represented.

If we are given certain simple problems to solve which depend on memory, the time to solvethem should reflect the structure. Perhaps we can gain some insight into the structure of memoryby these tasks. Conceptual analysis and e%perimental research based on the times to do some of

these tasks have been used to generate theories both about the structure of memory and about the

process of memory search.

4. Let us consider the words canary, robin, )enguin,and)iano. As speakers of /nglish we

know many things about canary. *e know that it refers to a kind of bird. *e know that

the thing it refers to is often yellow, has wings, has a heart, and is warmblooded. *eknow that canaries fly, sing, and lay eggs. *e know that a robin is a kind of bird, is

warmblooded, has a red breast, flies, has a heart, eats worms and lays eggs. *e know

that a penguin is a kind of bird, is warmblooded, swims, eats fish, and lays eggs. *e

know that the kind of ob&ect)ianorefers to, is +uite different from all of these.0. Kow do we represent the knowledge that we all have about words( An important idea

that is shared by many cognitive psychologists and other cognitive scientists is that

concepts which are related meaningfully with one another are linked in some kind of anetwork. /ach concept can be considered a 6node6 and the relation between them an arc.

. "here are many redundancies, and we know of many relationships among different

concepts. 'oes that mean that words with similar meanings are in some sense share partsof their meaning representation( :y what process or algorithm do we identify appropriate
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relationships( In order to demonstrate our knowledge, either directly by answering

+uestions about it, or indirectly, by using the meaningful information appropriately, we

must have access to and be able to operate on the right information.

3. X4, X0, and X lead us to consider how le%ical information is structured in memory and

what the processes are that we use to interrogate that memory. *e certainly feel that some

of the things that we know about these concepts we did not learn directly, but we couldfigure it out. ;rom a reasoning or problem solving, or computational perspective, we have

to be able to identify some procedure recursive process! which can effectively do the

task.

. Le%ical items are of various sorts. "he parts of speech in grammar help somewhat, but

does not designate all of the differences that seem to e%ist. Content words such as nouns,

verbs, and ad&ectives function differently from function words like prepositions,

pronouns, and con&unctions. /ach of these categories have words which functiondifferently from one another. I am particularly interested in the fact that some nouns are

:asic Level words. /%amples in urban American /nglish are chair, wall, tree, dog. "hese

seem to have a special status, probably due to their means of ac+uisition. "hey tend to be

learned directly from e%amples. 7ther level words, such as ;urniture, animal, and


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*hy do the same arcs have different response latencies( Category members do not all

function e+uivalently. It is faster to agree that 6a robin is a bird6 than that 6a chicken is a

bird6. "he closer in meaning two terms are, the faster you can categori@e the member.

Some links, which logically should be closer, take more time than those further away. It is

faster to respond that a lion is an animal, than that a lion is a mammal. ;re+uency of use

is a strong variable in reaction time studies.Some additional data

Sub&ects can identify a word as a word faster, if they are first presented with another word

that is similar in meaning to it. "he first word is the 6prime6 and the second is the target6. Ifthe word is unrelated, it does not decrease the identification time. In a 6le%ical decision

task6 sub&ects are to decide whether a letter string is a word or not. "his seems to work for

+uestion answering also. "hese data suggest that words which are related to one another

are tied together in some way) perhaps stored near each other in the brain, or are linkedsuch that when one is activated it activates similar items.

Psy 416: Reasoning and Pro#lem Solving

Sc"ema t"eory/rwin SegalPsy 345 Syllabus

"he le%icon seems to relate to what has been called le%ical or conceptual meaning. "his gives

what is usually called the meanings of the words. *hen, however, words are used to talk about

something or to refer to something we seem to enter a different ballgame. Certain phrases oftenrefer to things other than themselves, and sentences can be used to make assertions, ask

+uestions, re+uest activities, promise something, create a mood, tell stories, etc. *e will not deal

with many of these issues in this class, but one aspect of the more global properties of languagewill be used, either as a metaphor, or directly, for other reasons. $uch language is conte%tually

interpreted. "hat is, it relates to some integrated and usually! coherent domain, and only makes

sense within that domain. 7ur current term for this domain to which the discourse relates is

schema pluralschemata!.

Some properties of schemata or issues relating to schema theory

4. Conceptual structures that help us understand, interpret, and remember incoming

information

0. ?elated to


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:ransford et al) and 8ohnson washing clothes,serenading, sentential images,

conte%t sensitivity for interpretations

:ransford and ;ranks larger units) 7ne doesn6t recogni@e particular sentences, but

compares them to #full schema.# discussion

7ther :ransford remember particular sentences that fit into the frame. discussion

:eth Loftus remembering as a function of the +uestions asked or the conte%t.Childhood se%ual abuse repressed and then remembered


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If we focus on the process of becoming an e%pert rather than the claim that only a few become

e%pert, we may come to a position I first heard from $icki Chi. Children are universal novices.

"hey have not developed very many of the component skills needed for any domain. Decalageisthe order of the day) many of the skills needed are relatively domain specific. "he topics in the

topics of cognitive development are a selection of the topics that could be studied under the

rubric of e%pertise. ;ollowing Qygotsky, people learn to perceive and think in the domains thatthey come into direct interaction with. Some skills are fairly general in that they underlie many

other skills. "hose are the ones that children tend to learn first.

'omains that show movement from novice to e%pert include *alking, talking, reading /nglishte%t, writing, riding a bicycle, driving a car, getting around campus, talking to friends, studying

particular courses, taking notes, seeing mathematical relationships, understanding formal

arguments, taking multiple choice tests, taking essay tests. As we develop skills in these areas the

structure of our performance changes.

+ypothesis: "he development of e%pertise parallels the development of cognition in children.

As people develop e%pertise their skills and performance becomes structurally different

than it was prior to that development. "he performance of e%perts is +ualitatively

different from those of novices. *hen one learns a new task she is automatically at anearly stage of development. Kow early depends to a great e%tent on how many of the

component skills have already been developed.

Some e%amples*hat is a domain(! playing chess, looking at blood slides, listening to

music, looking at an %ray, looking at ' pictures, riding a bicycle, skiing. dancing,

gymnastics, solving physics problems, walking, reading, riding a bicycle, driving a car,dancing, typing, computer programming, cab driving, radiology, medical diagnosis,

playing a piano, violin, basketball, baseball, football, gymnastics, golf, writing papers,

taking tests.

Propositional 0nowledge--Philosophicallyknowing what. *hen novices learn in a newdomain, the information tends to be represented as independent single propositions, with the

development of e%pertise the separate pieces become integrated into larger units.

$ayer6s categories of propositional knowledge and comments

6inds of propositional 0nowledgea! factuale.g. e+uations, b! syntacticrecogni@e

appropriate forms, c! semantice.g. physical world, d! schematice.g. structural relations

among parts and types, e! strategice.g. approach to solving problems

I am not real happy about the five categories of knowledge that $ayer uses. Its not a bad first

step, but I have some problems with it. $ore now that I am more of an e%pert than when I

first encountered it. Particularly, I have trouble understanding $ayer6s difference between

Hactualand Semanticknowledge. :oth of these refer to having some knowledge of the'omain under study.

"he richness of understanding grows with the gaining of e%pertise. "he schemata that one

uses to account for the empirical observations get larger and more interconnected.

Syntacticknowledge could be the learning of e+uations, vocabulary, abbreviations,

symbols, particular forms of acceptable sentences, etc.

Semanticknowledge in the linguistic sense is knowing how to map the words, sentences,and e+uations onto the domain. "his is not easy. After identifying the basic laws of

motion 9ewton spent years trying to apply them to different domains and other physicists

continued that process for two hundred more years.

Schematicknowledge looks at the domain and identifies similarities and differences


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among parts. *hat is deemed similar often changes as one gains e%pertise. As stated in

the te%t, novices are much more likely to be captivated by surface similarities and e%perts

abstract or implicit ones.

Strategic 0nowledgeis more similar to proceduralknowledgeknowing how. Kow one

is likely to attempt to solve a problem is likely to vary as a function of the e%perience one

has with the domain. As one becomes more familiar she is much more likely for 6obvious6problems solve them by forward chaining or working forward. Kowever, the data for real

problems, i.e., problems of a type that the e%pert has not previously seen, are not likely to

be solved by forward chaining, but by some variant of meansends analysis.

Procedural 0nowledgeproduction systems, performance, skills, philosophically knowing how)

Procedurali8ationlearning how to do what needs to be done) and also with practice being able

to integrate what was originally separate implementations of procedures into larger performance

units.

If a problem has intermediate states, or if there are more than one or two operations,

selecting a correct procedure can be a daunting task. Intermediate feedback from the

system or from an e%ternal source may be necessary for improved performance.

If the specific procedure is unavailable, the problem solver may find himself in a state ofunknowing or frustration. Segal calls this an inchoate state.

/%perts know the voca#ularyof a particular domain. Some of it is +uite speciali@ed. "his#&argon# allows the specialist to combine several logically independent concepts into a single

unified whole. "he novice often can not learn the &argon even when she hears it, because the

components do not make a meaningful unit to her. So even the vocabulary implies anunderstanding of the structure of the domain. 6?enege6, in :ridge) 6Castle6 in chess) 6decalage6 in

Piaget6s theory) 6Power6 in statistics) 6Church"uring thesis6 in computation to name a few. "he

greater the e'pertise the larger the voca#ulary, and the better the understanding of the

underlying schema that the terms abstract from.

Syntactic knowledge is knowing the forms of the domain. "his might be the vocabulary, the

e+uations, the sentences.

"wo kinds of e%pertise, routineand adaptive, have been identified by some 8apanese scholarsKatano and Inagaki 4R5!!. ?eferenced in Kolyoak6s chapter, p 4D, in /ricsson B Smith 44!!.

?outine e%perts solve familiar problems +uickly and accurately. If the problems are unfamiliar

they may have trouble with them.

Adaptive e%perts can invent new procedures which vary from their basic methods. "hey might bethe 6creative6 e%perts. Kow one learns what to do is at least one important variable affecting this

difference. "rying to understand why the methods work help lead to adaptive e%pertise. "his is

reminiscent of *ertheimer and


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skills can be decomposed into simple enough parts that they are known a priori) however,

e%pertise still re+uires integrating and restructuring them into usable schemata.

*hat is the state of novice performance( Inchoate states, random trial and error, frustration,backward chaining, small units, surface form, separate nonintegrated components, bottomup

/%pert performancefocused, much forward chaining, topdown, coherent and integrated,

abstract organi@ation, large units, procedurali@ation, integrated se+uences, skillful, selective./ricsson, J. A. 45!. The road to e*cellence. $ahwah, 98 /rlbaum

Sternberg, ?. 8. B :enYeev, ". 0DD4! Com)le* Cognition/ The )sychology of human thought.

9ew Tork 7%ford.

Psy 416: Reasoning and Pro#lem Solving&reativity

/rwin Segal

(hat is !reativityBIt is hard to pin down e%actly what is to be studied in the psychological

study of creativity. Is creativity a mysterious +uality that some people seem to have, a gift fromthe gods, as the author of 6Amadeus6 seemed to think about $o@art( Is creative thinking a kind of

thinking that is different from ordinary problem solving and reasoning( Is creativity due tomotivational properties, educational e%perience, intelligence, social environment, somethingelse, or some combination of these( 'ifferences of opinion, and differences of methods to study

creativity abound.

(ho is creativeB Specific people have been identified by biographers, playwrights, and othersas being outstanding creative people, usually because their performances or products have been

deemed creative. Literature generally identifies certain inventers, scientists, musicians, artists,

writers, etc. "here is certainly no unanimity as to who should be so designated, but names that

come to mind include Simone de :eauvoir, Pablo Picasso, Ale%ander Calder, 8ames *att, 8ames*atson, 8ohannes


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huge number of hours devoted to the task at hand. Csiks@entmihalyi 4RR, 4D! calls such an

optimal e%perience #flow.# "he activity is engrossing and its own reward.9otes on inventors

Some general 3uestions about creativity

!an creativity #e measuredB"here is evidence that creativity is not the same thing as

intelligence. ?eports are that one needs to be relatively intelligent to be creative, but note%tremely so. "he reports are that there is no correlation between intelligence and creativity, once

IG is above about 40D.


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are not clear. Someone has to argue that a solution is creative and convince others that the

argument is sound. "hus, in order for someone to be deemed creative, or a genius, her

performance or portfolio has to find an audience who makes that &udgment. *ithout such anaudience that person or work might be &udged as merely competent, or even pedestrian.

Is creativity e'pertise plus something elseB7ne possible take on the idea of creativity is that a

creative individual is someone who is an e%pert in a domain, with the same set of conditions thatare necessary to establish e%pertise hard work, dedication, enthusiasm, selfconfidence, practice

and training. "o be creative, however, there may be a particular kind of perspective that one takes

on problems. "his is what training in creativity tries to teach, but as with all important thinking,it must be done on top of background skills developed within a particular domain.

?ead the chapter in *eisbergthat is on reserve. *eisberg argues that the novelty that is

associated with creative geniuses is of e%actly the same type as other 6normal6 thinking.

Csiks@entmihalyi, $. 4D!.Flo#/ The )sychology of o)timal e*)erience.9ew Tork Karperand ?ow.

Csiks@entmihalyi, $. B Csiks@entmihalyi, I. /ds.! 4RR!. 0)timal e*)erience.9ew Tork

Cambridge -niversity Press.


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*hat does an agent know(

Kow does the agent ac+uire knowledge(

Kow is knowledge represented in the agent(

Kow does the agent use that knowledge for reasoning or action(

II. Alternate viewpoint

Some cognitive scientists argue that the particular actions and decisions that are made are moreintimately involved with aspects of the situation than is obvious from the usual focus on the

agent.

Situation centered views of problem solving have been gradually gaining steam. "hey go byvarious names and there is no consensus of what it is all about, but there is definitely some

important issues involved. "he broad issue is the belief that properties of cognition, as well as

details of behavior, depend a great deal on details of the conceptual, social, cultural, or physical

conte%t. "here is often an interplay between the conte%ts and the cognition that would not bediscovered without broadening the analysis.

"he units to be studied as cognitive systems are thus are not individual agents or minds, but

individuals in different conte%ts. "he Ceci and ?oa@@i chapter on reservegives e%amples and

data on how conceptual and cultural conte%ts have ma&or influences on what effective procedurescan be accessed in dealing with certain tasks. "he /d Kutchins article on reservedescribes a

cognitive analysis of a commercial airliner6s cockpit. ;rom this perspective problem solving doesnot reside in the head, but rather resides in a dynamic interaction between the person and the

environment. :y enlarging the unit for cognition we increase the likelihood that we can see the

dynamic interplay of internal and e%ternal properties of the system. Importantly, even thealgorithms and heuristics used by the system are not the same as those that a researcher might

propose if she considered the agent independently of the system.

Some pro#lems which seem to reuire analytic analysis of conte'ts to fully e'plain.

4. Subtracting one multidigit number from another.

0. :uilding a house of cards

. *riting a paper on creativity

3. Landing an airplane without crashing

. Playing in the violin section of an orchestra

5. ;inding the coefficient of friction in a physics problem

M. 'ocking an Aircraft Carrier

*hat e%ternal props are used to solve the problems(

*hat roles do they play(

/d Kutchins asks #Kow many people on an Aircraft Carrier actually know how to dock it(#

"he answer he gives is #9one.#

"his does not mean that the carrier never docks, but rather that the knowledge of how to dock it

is distributed over several participants in the activity, each of whom knows what he is to do andhow and when to do it. "he unit to study to understand the problem of docking an aircraft carrier

is the aircraft carrier being docked, and the roles of the people involved.

!onsider the role of different conte'ts in pro#lem solving.
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4. If two people, A and :, work on a problem together A can add to what : has done #on

line.# "he contribution by A to the solution may have been something that was not in the

problem solving schema that she had available until the new information was received.;urthermore, her own idea might not have made sense to her without the information

received from :.

0. $ost people who write papers, music, or poetry, edit their works. "hey generate it andthen evaluate the results and modify it. "he drafts serve as inputs to the process and are

part of the problem domain. /ffective procedures include recursively reading what has

&ust been written, evaluating it, and editing it. 7bviously the manuscript being revised ispart of the system needed to understand the effective procedures used to solve the

problem.. In the assigned An@ai article, how the problem solvers developed and used diagrams

played an important role in solving the problems. ;rom the perspective taken here, thediagram is part of the system solving the problem. Kaving the diagram changes the

details of the algorithm used to solve the problem. Algorithms often include e%ternal

diagrams.

3. If someone has a logic problem to solve, e.g. the 6'onald1


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"he bottom line is that reasoning and problem solving is often conte%tuali@ed and there

are pressures to make both the internal computations or memories less difficult and to

make use of physical and social inputs that are available. Cultural differences in "hinking

!onceptual and *otivational Influences on Pro#lem Solving

4. Predict location of geometric shapes or play video game with same algorithm0. Predicting races or stock markets

. Add numbers or price sets of products "hese are reported in Ceci and ?oa@@i! 3. African American students, /ast Asian students, and *omen taking tests at ma&or

universities.

return to syllabus

Psy 1;:$easoning and Pro#lem Solving

/rwin Segal

Intelligence)

istory"he idea that there are individual differences in some kinds of cognitive skills is probably a veryancient notion, although historically it was very confused. "he idea of intelligence differenced

got a strong boost from Hrancis Galton, Charles 'arwin6s cousin, and it evolved as a

conse+uence of the theory of evolution. $embers of a species are not all alike.


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with correlated gene structure( "he data supporting some view like this seem +uite strong, but[

Sternberg review of the :ell Curve. I suggest that you read this discussion.

7ther researchers using other principles of factor analysis came up with different analyses. 7ne,which has had considerable influence is that of "hurstone 4R!, who identified several

primary mental a#ilitiesorgani@ed around content and performance areas. "he ones most

widely cited include Ver#al comprehensionvocabulary, verbal analogies, readingcomprehension!, ver#al fluencyanagrams, naming words in a category, rhyming!, num#er

speed and accuracy of simple computation!, memory short term, strings of numbers, words or

faces, note se+uences!) perceptual speedproofreading, matching symbol strings, findingidentical pictures!) Induction number series, word classifications, finding odd word in a group!)

spatial visuali8ationrotating figures, folding bo%es!

?aymond Cattell proposed two generali@ed aspects of intelligence 4! Hluid intelligencefigural

analogies, series completion, and classification. 0! !rystalli8ed intelligence vocabulary, generalknowledge, reading comprehension

Some psychometric views combine factors in a hierarchical intelligence, g, in con&unction with

group and specific factors, or gcombined with crystalli@ed and fluid abilities.

7ne scholar, 8. P.


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surgeons, dancers, choreographers, and crafts people!

5! Interpersonalawareness of others6 feelings, emotions, goals, motivations "eachers,

parents, politicians, psychologists, and salespeople!

M! Intrapersonalawareness of one6s own feelings, emotions, goals, motivations

psychologists, novelists!

R! 9aturalistnew! recognition and classification of ob&ects in the environment ;armers,gardeners, botanists, geologists, florists, and archaeologists !.


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*hat is the role of maturation and what is the role of e%perience in the development of

intelligences!( "o what e%tent can e%periences substitute for innate properties(

All intelligent behaviors re+uire a se+uence of processes. Any of these may have an individualdifference component. Intelligent behaviors re+uire search, recognition, identification, selection,

memory, knowledge, concentration, planning, evaluation, decisions, e%ecution skill, comparison,

motivation, etc.

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Segal Logical Concepts