Ian Stewart

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Directly Trained Baseline Relations

Derived Symmetrical Relations

Derived Transitive Relations Derived Equivalence Relations

A B CSymmetry Symmetry

Equivalence

Transitivity

A Schematic Representation of Stimulus Equivalence

Derived Relations

A

B C

Why the interest?1. Untrained Performances

• Emergent

• Derived

• Generative

2. Difficult to explain using traditional behavioural concepts

3. Relevant to human language and cognition

Non-Humans and Derived Relations

• Apparently absent in nonhumans

• Present in all normal humans

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Baboon 1 Baboon 2 Rhesus 1 Rhesus 2 Child 1 Child 2

Per

cent

Cor

rect

Performance on Tests for Symmetry Responding

Sidman et al. (1982)

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60

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100

Lana Sherman

Per

cent

Cor

rect

Performance on Tests for Symmetry Responding

Dugdale & Low e (2000)

Non-Humans and Derived Relations

C1

A1 A2

A goes with B and B goes with blah,

blah, blah . . . Who cares, I’m a duck!

Non-Humans and Derived Relations

If A goes with B, then B goes with

banana? Doh! Got it wrong again.

Emerges in infancy Emerges in infancy in humansin humans

0

50

100P

erce

nt

corr

ect

Learn Object-Name, Test Name-ObjectAge: 17 months

87.5%(4 pairs)

Lipkens, Hayes, & Hayes (1993)

Development and Derived RelationsDevelopment and Derived Relations

Emerges in infancyEmerges in infancy Can combine multiple Can combine multiple

relations at least by relations at least by 23 months23 months

Object Name

Sound 0

50

100

Per

cen

t co

rrec

t

Name-SoundSound-Name

Age: 23 months

90%(4 pairs)

Lipkens, Hayes, & Hayes (1993)

Development and Derived RelationsDevelopment and Derived Relations

Emerges in infantsEmerges in infants Can combine multiple Can combine multiple

relations at least by relations at least by 23 months23 months

Multiple relational Multiple relational forms develop in forms develop in infantsinfants

020406080100

Per

cen

t C

orr

ect

16 24 26 27

Age in Months

Expose Novel Name-Picture

Test Novel Picture-Name

Lipkens, Hayes, & Hayes (1993)

Development and Derived RelationsDevelopment and Derived Relations

Development and Derived RelationsDevelopment and Derived Relations

Emerges in infantsEmerges in infants Can combine multiple Can combine multiple

relations at least by 23 relations at least by 23 monthsmonths

Multiple relational forms Multiple relational forms develop in infantsdevelop in infants

Correlates with Correlates with cognitive/verbal abilitycognitive/verbal ability

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25

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75

100

1 2 3 4Blocks of Testing (No

Feedback)

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cent

age

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rect

LD: No receptive

LD: Receptive

Normal

Devany, Hayes, & Nelson (1986)

Chance

Development and Derived RelationsDevelopment and Derived Relations

Emerges in infantsEmerges in infants Can combine multiple Can combine multiple

relations at least by 23 relations at least by 23 monthsmonths

Multiple relational forms Multiple relational forms develop in infantsdevelop in infants

Correlates with Correlates with cognitive/verbal abilitycognitive/verbal ability

Correlates with the Correlates with the development of specific development of specific verbal skillsverbal skills

Barnes, McCullagh, & Keenan (1990)

0

25

50

75

100

1 2 3 4Blocks of Testing (No

Feedback)

Per

cent

age

Cor

rect

Normal

Hearing Impaired:Language =>2 yrs

Chance

Hearing Impaired: Expressive NamingNo Receptive Naming

Language and Derived RelationsLanguage and Derived Relations

Derived relations Derived relations correlate with verbal correlate with verbal ability on the WAISability on the WAIS

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Low Verbal Scores High Verbal Scores

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cent

Cor

rect

Pelez-Nouregas, O’Hora, & Barnes-Holmes (in press)

500

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Me

an

Mill

ise

con

ds

Priming Among Equivalent and Non-Equivalent Stimuli

Reaction Time

Directly Trained

Symmetry EquivalenceEq. Member - Nonmember

Eq. Member - Nonsense

Nonsense - Eq. Member

Nonsense - Nonsense

Transitivity

Language and Derived RelationsLanguage and Derived Relations

Derived relations Derived relations correlate with verbal correlate with verbal ability on the WAISability on the WAIS

Derived relations Derived relations produce priming effectsproduce priming effects

Staunton, Barnes-Holmes, Whelan, & Barnes-Holmes (2002)

Language and Derived RelationsLanguage and Derived Relations

Derived relations Derived relations correlate with verbal correlate with verbal ability on the WAISability on the WAIS

Derived relations Derived relations produce priming effectsproduce priming effects

Derived relations Derived relations produce differential produce differential ERPs measuresERPs measures

McIlvane, et al. (1999)

Language and Derived RelationsLanguage and Derived Relations

Derived relations correlate Derived relations correlate with verbal ability on the with verbal ability on the WAISWAIS

Derived relations produce Derived relations produce priming effectspriming effects

Derived relations produce Derived relations produce differential ERPs measuresdifferential ERPs measures

Derived relations produce Derived relations produce neural activation patterns neural activation patterns (recorded using fMRI) that (recorded using fMRI) that resemble those involved in resemble those involved in semantic processingsemantic processing

Dickins, Singh, Roberts, Burns, Downes, Jimmieson, & Bentall (2001)

Equivalent

This model captures one of the ‘core’ properties of analogy -- the relating of relations

If derived relations provide a behavioral model of semantic relations, then the relating of derived relations to derived relations may provide a model of analogical reasoning

APPLE

SHEEPPEACH

DOG

Equivalence-Equivalence Equivalent

So What About Analogy?

Stewart, Barnes-Holmes, Roche & Smeets (2001) proposed a model of analogy as

equivalence-equivalence responding based on the abstraction of common physical properties

However, analogy is not simply relations between arbitrary relations. Analogies are useful because they abstract out non-arbitrary relations between events. In other words,

analogy has its origins in the control of behavior by non-arbitrary environmental relations

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Test 1 -- ‘Property Abstraction’

Test 2 -- Equivalence-Equivalence

Z1

W2W1

Z2

W1 W2

W1/Z1

Y1/X2Y2/X2

W1/Z2

Y1/X1 Y2/X1

The two central features of this theoretical and empirical model of analogy are as follows:

(i) Relations between relations

(ii) The relations to be related involve non-arbitrary properties

Stewart, Barnes-Holmes, Roche and Smeets (2002)

2 --- Training and Testing of four 5-member EQUIVALENCE relations

1 --- BASELINE Block Sorting Task

4 --- Test for the discrimination of formal similarity

3 --- EQUIVALENCE-EQUIVALENCE Testing, biasing towards color or shape

5 --- Block Sorting Task testing for TRANSFORMATION OF FUNCTION

?

?

?

Stage 1 - Block Sorting

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Stage 2 - Equivalence Training & Testing

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Stage 3 - Equivalence-Equivalence Testing

Equivalence-Equivalence

Discrimination of FormalSimilarity (“Insight”)

B1/C1

B3/C3 B2/C4

Equivalence-Equivalence Testing (Shape-Bias)

Equivalence-Equivalence

Discrimination of FormalSimilarity (“Insight”)

Color

Color Color

Color

Shape

ShapeShape

Shape

Stage 4 - Test for Discrimination of Formal Similarity

COLOUR GROUP

SHAPE GROUP

Stage 5 - Transformationof Function

Cognitive Development, Analogy and Derived Relations

• If the current model of analogical reasoning has some validity, equivalence-equivalence tests should produce outcomes similar to those observed with traditional tests of analogical reasoning

• Adults and older children readily demonstrate analogical reasoning

• Young children (4-5 year olds) do so less readily, and when they do some researchers have argued that the performances are primarily associative or thematic rather than analogical

• Recent research has examined developmental differences in equivalence-equivalence responding in order to assess the validity of the model

Stage 1 – Equivalence Training and Testing

Stage 2 – Equivalence-Equivalence Testing with No Associative comp.

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B3C3 B2C3

Stage 3 – Equivalence-Equivalence Testing With Associative comp.

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Equiv Equiv-Equiv

9-yr Olds Equiv Equiv-Equiv

Adults Equiv Equiv-Equiv

5-yr Olds

Participants Who Passed the Equivalence and Equivalence-Equivalence Tests

Carpentier, Smeets, & Barnes-Holmes (2002)

Experiment 1

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Stage 1 – Equivalence Training and Testing

Stage 2 – Equivalence-Equivalence Testing with No Associative comp.

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Stage 3 – Equivalence-Equivalence Testing With Associative comp.

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Experiments 2 & 3 Perhaps the 5-year olds failed to treat the BC compound stimuli as functionally equivalent to the corresponding sample-comparison configurations? Extra trial-types were inserted after (Exp 2) or before (Exp 3) a child failed an Equiv-Equiv test.

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+

Carpentier, Smeets, & Barnes-Holmes (2002)

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)Participants Who Passed the Equivalence and Equivalence-Equivalence Tests

Equiv Equiv-Equiv

Adults Equiv Equiv-Equiv

9-yr Olds Equiv Equiv-Equiv

5-yr Olds

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Stage 1 – Equivalence Training and Testing

Stage 2 – Equivalence-Equivalence Testing with No Associative comp.

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Stage 3 – Equivalence-Equivalence Testing With Associative comp.

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B1C2

B2C2 B2C3

Experiment 4 Perhaps the 5-year olds failed the Equiv-Equiv tests because they did not encounter this particular task format until they were presented with the test? If so, test exposures to AB-AB and AC-AC matching tasks should remedy this problem.

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A3B3 A3B2

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A3B3 A3C2

Carpentier, Smeets, & Barnes-Holmes (2002)

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No.

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Equiv Equiv-Equiv 5-yr Olds

Participants Who Passed the Equivalence and Equivalence-Equivalence Tests

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Stage 1 – Equivalence Training

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Stage 2 – Equivalence-Equivalence Testing with No Associative comp.

B1C1

B3C3 B2C3

Stage 3 – Equivalence Testing

B1C2

B3C3 B2C3

Experiments 5 - 8 Given that 5-year olds can pass an Equiv-Equiv test following exposure to AB-AB and AC-AC matching tasks, could they also pass this test BEFORE being exposed to an Equiv test? Barnes et al., (1997) demonstrated this with adults.

A3B1

A3B3 A3B2

A1B1

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No Equivalence Test

No Equivalence Test

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Participants Who Passed the Equivalence-Equivalence Test Before and After Passing the Equivalence Test

Equiv-Equiv Equiv-Equiv Before Equiv After Equiv Adults

Equiv-Equiv Equiv-Equiv Before Equiv After Equiv

5-Year Olds

Carpentier, Smeets, & Barnes-Holmes (in press)

So What?• These findings are broadly consistent with previous

research on analogical reasoning in children and adults

• Adults and older children demonstrated equivalence-equivalence responding with relative ease but the 4-5 year olds did not

• However, the 5-year olds readily demonstrated equivalence-equivalence responding following, but not proceeding, a successful equivalence test

• What does this mean?

So What?• Some developmental/cognitive researchers have argued

that when a young child solves a verbal analogy the solution is “primarily but not exclusively associative” (Sternberg & Nigro, 1980, p. 36; see also Gentner, 1989)

• Others have argued that genuine analogical reasoning “is an important building block from an early age” (Goswami & Brown, 1990, p. 207)

• The extent to which the current behavioural data support one of these positions depends on what is meant by “associative”

So What?• If associative means based on directly taught,

reinforced, or explicitly instructed stimulus pairings, then the current data refute the former position

• The 5-year olds clearly demonstrated equivalence-equivalence responding based on untaught or derived equivalence relations

• If associative means based on stimulus pairings that occur either via direct reinforcement or derivation the data appear to support the former position rather than the latter

• Almost all of the 5-year olds required an equivalence test, during which the derived “associations” could occur, before successfully passing the equivalence-equivalence test

Ian Stewart

Thus far we have provided basic behavioral models that capture some of the core features of both

analogy and metaphor

However, what about differences between these phenomena?

For example, one important difference may be that analogy is bidirectional, whereas

metaphor is unidirectional

M E T A P H O RA N A L O G Y

“An atom is like the solar system”

ATOM SOLAR SYSTEM

ATOMSOLARSYSTEM

(A)

(B)

e-

“Cats are dictators”

CATS

CATSDICTATORS

(A)

(B)

A works . . . but B doesn’t

DICTATORSObvious qualities:

Small, furryNon-obvious

qualities:

Demanding, willful

Obvious qualities:

Demanding, willful

Obvious qualities: Demanding, willful

Obvious qualities: Small, furry

Non-obvious qualities:

Demanding, willful

Modeling analogy and metaphor - An overview of progress so far

--- Barnes, Hegarty and Smeets (1997) provided a model of analogical reasoning as equivalence-equivalence

responding

--- Stewart, Barnes-Holmes, Roche & Smeets (In press) provided a more ecologically valid model of analogy as

equivalence-equivalence responding based on the abstraction

of common formal properties

--- In more recent research in the Maynooth laboratory, we have modeled the experience of “insight”

provided by metaphor and analogy

--- We are presently working with a procedure (the Relational Evaluation Procedure or REP) that will allow us to examine

multiple types of relations in the context of analogy and metaphor (e.g., unidirectional relations)