1. Ian Stewart

4. A1 B2B1 A2 B2B1 C2C1 B2 C2C1 B1 A2A1 B2 A2A1 C1 B2B1 C2 B2B1 A1 C2C1 A2 C2C1 A2A1 C2 A2A1 Directly Trained Baseline Relations Derived Symmetrical Relations Derived Transitive RelationsDerived Equivalence Relations

5. ABC Symmetry Equivalence Transitivity A Schematic Representation of Stimulus Equivalence

6. Derived Relations A BC Why the interest? 1.Untrained Performances Emergent Derived Generative 2.Difficult to explain using traditional behavioural concepts 3.Relevant to human language and cognition

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

8. 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!

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

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

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

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

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

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

15. Language and Derived Relations Derived relations correlate with verbal ability on the WAIS 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 correlate with verbal ability on the WAIS Derived relations produce priming effects 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 correlate with verbal ability on the WAIS Derived relations produce priming effects Derived relations produce priming effects Derived relations produce differential ERPs measures 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 correlate with verbal ability on the WAIS Derived relations produce priming effects Derived relations produce priming effects Derived relations produce differential ERPs measures Derived relations produce differential ERPs measures Derived relations produce neural activation patterns (recorded using fMRI) that resemble those involved in semantic processing 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. 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?

20. 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

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

22. Test 1 -- ‘Property Abstraction’ Test 2 -- Equivalence-Equivalence Z1 W2W1 Z2 W1W2 W1/Z1 Y1/X2 Y2/X2 W1/Z2 Y1/X1Y2/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) 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

25. ? ? ? Stage 1 - Block Sorting

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

27. B1/C1 B2/C2B3/C4 Stage 3 - Equivalence-Equivalence Testing Equivalence-Equivalence Discrimination of Formal Similarity (“Insight”)

28. B1/C1 B3/C3B2/C4 Equivalence-Equivalence Testing (Shape-Bias) Equivalence-Equivalence Discrimination of Formal Similarity (“Insight”)

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

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

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. Stage 1 – Equivalence Training and Testing Stage 2 – Equivalence-Equivalence Testing with No Associative comp. B1C1 B3C3B2C3 Stage 3 – Equivalence-Equivalence Testing With Associative comp. B1C1 B3C3B1C3 B1C2 B3C3B2C3 B1C2 B2C2B2C3 Carpentier, Smeets, & Barnes-Holmes (2002) Experiment 1 B1 B2 B3 C1 C2 C3 A1 A2 A3

33. Stage 1 – Equivalence Training and Testing Stage 2 – Equivalence-Equivalence Testing with No Associative comp. B1C1 B3C3B2C3 Stage 3 – Equivalence-Equivalence Testing With Associative comp. B1C1 B3C3B1C3 B1C2 B3C3B2C3 B1C2 B2C2B2C3 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. B1C1B3C1B1C3 B1 C1C2C3 + Carpentier, Smeets, & Barnes-Holmes (2002) B1 B2 B3 C1 C2 C3 A1 A2 A3

34. Stage 1 – Equivalence Training and Testing Stage 2 – Equivalence-Equivalence Testing with No Associative comp. B1C1 B3C3B2C3 Stage 3 – Equivalence-Equivalence Testing With Associative comp. B1C1 B3C3B1C3 B1C2 B3C3B2C3 B1C2 B2C2B2C3 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. A3B1 A3B3A3B2 A1B1 A3B3A3C2 Carpentier, Smeets, & Barnes-Holmes (2002) B1 B2 B3 C1 C2 C3 A1 A2 A3

35. Stage 1 – Equivalence Training B1 B2 B3 C1 C2 C3 A1 A2 A3 Stage 2 – Equivalence-Equivalence Testing with No Associative comp. B1C1 B3C3B2C3 Stage 3 – Equivalence Testing B1C2 B3C3B2C3 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 A3B3A3B2 A1B1 A3B3A3C2 B1 C1C3C2 B3 C1C3C2 No Equivalence Test Carpentier, Smeets, & Barnes-Holmes (in press)

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

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)