Ian Stewart

1. Analogical Reasoning Contributions from Behavioural Psychology Ian Stewart

2. Wrong! Wrong! Correct! Correct!

3. Correct! Correct! Symmetry! Symmetry!

4. Directly Trained Baseline Relations A1 A2 B1 B2 B1 B2 B1 B2 C1 C2 C1 C2 B1 A1 A2 B2 C1 C1 C2 C2 C1 A1 C2 A2 C1 A1 C2 A2 A1 B1 B2 A2 B1 A1 B2 A2 Derived Symmetrical Relations Derived Transitive Relations Derived Equivalence Relations

5. A Schematic Representation of Stimulus Equivalence Transitivity A B C Symmetry Symmetry Equivalence

6. Derived Relations • Why the interest? • Untrained Performances • Emergent • Derived • Generative • Difficult to explain using traditional behavioural concepts • Relevant to human language and cognition A B C

7. Non-Humans and Derived Relations • Apparently absent in nonhumans • Present in all normal humans

8. Non-Humans and Derived Relations A goes with B and B goes with blah, blah, blah . . . Who cares, I’m a duck! C1 A1 A2

9. Non-Humans and Derived Relations If A goes with B, then B goes with banana? Doh! Got it wrong again.

10. Development and Derived Relations • Emerges in infancy in humans 87.5% (4 pairs) Lipkens, Hayes, & Hayes (1993)

11. Development and Derived Relations • Emerges in infancy • Can combine multiple relations at least by 23 months Object Name 90% (4 pairs) Sound Lipkens, Hayes, & Hayes (1993)

12. Development and Derived Relations • Emerges in infants • Can combine multiple relations at least by 23 months • Multiple relational forms develop in infants Lipkens, Hayes, & Hayes (1993)

13. Development and Derived Relations • Emerges in infants • Can combine multiple relations at least by 23 months • Multiple relational forms develop in infants • Correlates with cognitive/verbal ability Normal LD: Receptive Chance LD: No receptive Devany, Hayes, & Nelson (1986)

14. Development and Derived Relations • Emerges in infants • Can combine multiple relations at least by 23 months • Multiple relational forms develop in infants • Correlates with cognitive/verbal ability • Correlates with the development of specific verbal skills Normal Hearing Impaired: Language =>2 yrs Chance Hearing Impaired: Expressive Naming No Receptive Naming Barnes, McCullagh, & Keenan (1990)

15. Language and Derived Relations • Derived relations correlate with verbal ability on the WAIS Pelez-Nouregas, O’Hora, & Barnes-Holmes (in press)

16. Language and Derived Relations • Derived relations correlate with verbal ability on the WAIS • Derived relations produce priming effects Staunton, Barnes-Holmes, Whelan, & Barnes-Holmes (2002)

17. Language and Derived Relations • Derived relations correlate with verbal ability on the WAIS • Derived relations produce priming effects • Derived relations produce differential ERPs measures McIlvane, et al. (1999)

18. Language and Derived Relations • Derived relations correlate with verbal ability on the WAIS • Derived relations produce priming effects • Derived relations produce differential ERPs measures • Derived relations produce neural activation patterns (recorded using fMRI) that resemble those involved in semantic processing Dickins, Singh, Roberts, Burns, Downes, Jimmieson, & Bentall (2001)

19. So What About Analogy? 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 DOG Equivalence-Equivalence Equivalent Equivalent PEACH SHEEP This model captures one of the ‘core’ properties of analogy -- the relating of relations

20. 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 Stewart, Barnes-Holmes, Roche & Smeets (2001) proposed a model of analogy as equivalence-equivalence responding based on the abstraction of common physical properties

21. A2 W2 W1 A1 X1 B1 B2 X2 C2 Y2 Y1 C1 D2 Z2 Z1 D1

22. Test 1 -- ‘Property Abstraction’ Z1 Z2 W1 W2 W1 W2 Test 2 -- Equivalence-Equivalence W1/Z1 W1/Z2 Y2/X2 Y1/X2 Y1/X1 Y2/X1

23. 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

24. Stewart, Barnes-Holmes, Roche and Smeets (2002) 1 --- BASELINE Block Sorting Task 2 --- Training and Testing of four 5-member EQUIVALENCE relations 3 --- EQUIVALENCE-EQUIVALENCE Testing, biasing towards color or shape 4 --- Test for the discrimination of formal similarity 5 --- Block Sorting Task testing for TRANSFORMATION OF FUNCTION

25. Stage 1 - Block Sorting ? ? ?

26. Stage 2 -Equivalence Training & Testing B1 A1 C1 B2 C2 A2 B3 C3 A3 B4 C4 A4

27. Stage 3 -Equivalence-Equivalence Testing B1/C1 Discrimination of Formal Similarity (“Insight”) Equivalence-Equivalence B2/C2 B3/C4

28. Equivalence-Equivalence Testing (Shape-Bias) B1/C1 Discrimination of Formal Similarity (“Insight”) Equivalence-Equivalence B3/C3 B2/C4

29. Stage 4 - Test for Discrimination of Formal Similarity Color Shape Color Shape Color Shape Color Shape

30. Stage 5 - Transformation of Function COLOUR GROUP SHAPE GROUP

31. 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

32. Experiment 1 Stage 1 –Equivalence Training and Testing Stage 2 –Equivalence-Equivalence Testing with No Associative comp. Stage 3 –Equivalence-Equivalence Testing With Associative comp. B1 C1 A1 B2 C2 A2 B3 C3 A3 Carpentier, Smeets, & Barnes-Holmes (2002) B1C2 B1C1 B1C1 B3C3 B2C3 B3C3 B3C3 B1C3 B2C3 B1C2 B2C2 B2C3

33. Experiments 2 & 3 Stage 1 –Equivalence Training and Testing Stage 2 –Equivalence-Equivalence Testing with No Associative comp. Stage 3 –Equivalence-Equivalence Testing With Associative comp. B1 C1 A1 B2 C2 A2 + B3 C3 A3 B3C1 B1C1 B1C3 C1 C2 C3 B1C2 B1C1 B1C1 B1 B3C3 B2C3 B3C3 B3C3 B1C3 B2C3 B1C2 B2C2 B2C3 Carpentier, Smeets, & Barnes-Holmes (2002) 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.

34. Experiment 4 Stage 1 –Equivalence Training and Testing Stage 2 –Equivalence-Equivalence Testing with No Associative comp. Stage 3 –Equivalence-Equivalence Testing With Associative comp. B1 C1 A1 B2 C2 A2 B3 C3 A3 A1B1 A3B3 A3C2 B1C2 A3B1 B1C1 B1C1 B3C3 A3B3 B2C3 A3B2 B3C3 B3C3 B2C3 B1C3 B1C2 Carpentier, Smeets, & Barnes-Holmes (2002) B2C2 B2C3 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.

35. Experiments 5 - 8 Stage 1 –Equivalence Training Stage 2 –Equivalence-Equivalence Testing with No Associative comp. Stage 3 –Equivalence Testing B1 C1 A1 B2 C2 A2 B3 C3 A3 A1B1 A3B3 A3C2 B1C2 A3B1 B1C1 B3C3 A3B3 B2C3 A3B2 B3C3 B2C3 B1 B3 C1 C2 C3 C1 C2 C3 Carpentier, Smeets, & Barnes-Holmes (in press) 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. No Equivalence Test No Equivalence Test

36. 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?

37. 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”

38. 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

39. Analogical Reasoning Contributions from Behavioural Psychology Ian Stewart

40. 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

41. “An atom is like the solar system” “Cats are dictators” (A) (A) SOLAR SYSTEM CATS DICTATORS ATOM Obvious qualities: Small, furry Non-obvious qualities: Demanding, willful Obvious qualities: Demanding, willful (B) SOLAR SYSTEM (B) ATOM DICTATORS CATS e- Obvious qualities: Small, furry Non-obvious qualities: Demanding, willful Obvious qualities: Demanding, willful A works . . . but B doesn’t A N A L O G Y M E T A P H O R

42. 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)