A Naturalistic Exploration of the Forms and Functions of Analogizing Robert R. Hoffman Thomas K. Eskridge Institute for

2. A Naturalistic Exploration of the Forms and Functions of Analogizing Robert R. Hoffman Thomas K. Eskridge Institute for Human and Machine Cognition Cameron Shelly Dalhousie University The 9th bi-annual International Conference Naturalistic Decision Making London 23-26 June, 2009

3. Outline • Examples + History and Importance of the Concept • Analogy in Computer Science • Analogy in Psychology • A Taxonomy of Kinds • Implications + Innuendos

4. 1 : 2 :: 2 : 4 Circle : Sphere :: Triangle : Cone Analogos geometric or numerical proportions, ratios, or symmetries.

5. ATOMS ARE LIKE SOLAR SYSTEMS SUN - NUCLEUS PLANETS - ELECTRONS ORBITS - ORBITS

6. Analogy in science Sound moves in waves, like water (Vitruvius). A planet is a projectile (Galileo [?], Newton). Chemical elements can be arranged according to their properties like the suits in a deck of cards (i.e., periodic table) (Mendeleeff). Gasses are like a container of billiard balls (i.e., kinetic theory) (Boyle). Molecules can have shapes, such as that of a snake (Kekule). Division of the atomic nucleus is like cell fission (Frisch, Meitner). The heart is a pump (Harvey). The body/brain is a machine (de la Mettrie, Descartes, de Condillac). Society is like an organism (le Bon). Organisms are like a society (i.e., cell theory) (Virchow). The brain is like a telegraph/telephone switchboard (Helmholtz, Wundt). The mind-brain is a control mechanism (de la Mettrie, Wiener). The rational mind is a logical or symbol processing machine (Pierce, Boole, Newell, Simon, McCarthy, Feigenbaum, Minsky, etc., etc., etc.).

7. Scream : Screams : Screaming : Screamer : Screamed :: Dream : Dreams : Dreaming : Dreamer : Dreamed Middle Ages Grammarians – analogy as an explanation of historical change of word forms and inflections

8. POETICS JULIET IS LIKE THE SUN LARGE AND MADE PRIMARILY OF GAS?

9. A WOMAN WITHOUT A MAN IS LIKE A FISH WITHOUT A BICYCLE Middle Ages Rhetoricians – analogy on par with syllogism, a form of proper argumentation

10. ROBIN : BIRD:: MUSTANG : ____?_____

11. ROBIN : BIRD:: MUSTANG : ____?_____ • EUCARYOTE • VERTEBRATE • CHRONOCYCLELOGRAPH • MENTAL TEST

12. One Giant Leap for Mankind Analogy as a critical process in perception, language, learning, and problem solving OR Analogy as a “basic,” “fundamental,” or “irreducible” mental operation ??????

13. "Men reason by analogy long before they have learned to reason by abstract characters” (James, 1980, vol. 2, p. 363). "All expressions of mental phenomena are borrowed from analogous material in experience" (Höffding, 1904, p. 153). "Analogy is a primordial condition of all language” (Breal, 1964, p. 7).

14. "Analogy is ubiquitous in human thinking" (Thagard, et al, 1990, p. 259). "A faculty for analogical reasoning is an innate part of human cognition. The concept of an inferentially sound analogy is universal" (Gentner and Jeziorski, 1993, p. 447). "The ability to perceive similarities and analogies is one of the most fundamental aspects of human cognition" (Voisniadou and Ortony, 19089, p. 1).

15. "The basic constraints of analogy—similarity, structure and purpose —are already present in the chimpanzee... preschool children, without any formal training, have a natural capacity to reason by analogy... Analogical thinking is the product of evolutionary changes in the way animals represent knowledge of relations" (Holyoak and Thagard, 1995, p. 4, 67, 72). "Analogy is the core of cognition" (Hofstadter, 2001, p. 499).

16. Resemblance Theory Aristotle Physics (and other places) The general process of perceiving resemblances or similarities, especially similarity of function John Stuart Mill System of Logic (1982, Ch.20) “The resemblance of relations."

17. Analogy and Computer Science • Many dozens of attempts at computational modeling: • Story understanding • Theorem proving • Means-ends analysis in planning • The solving of letter string analogies • The solving of geometric analogies • Problem-solving in hydraulics, thermodynamics, process control • Automated deduction and machine learning

18. Nearly all computational models: • Hierarchies or graphs are matched on the basis of similarity • (shared features and shared relations). • Empty feature slots are filled by a process of mapping or • filtering. • Some process of restructuring of relations. • A distinction between features and relations. • e.g., atom-solar system example

19. Representational Techniques Production rules Symbolic-connectionst hybrids Bayes nets, etc.

20. Processing Approaches Some begin with elaborate memory representations. Some begin impoverished and build up representations. Some operate on individual analogies. Some construct complex domain-domain mappings based multiple analogs.

21. Processing Approaches Some models generate all possible mappings and then evaluate for coherence. Some restrict mappings to those that satisfy given a priori goals. Some systems remember all of their past failures. Some systems attempt to derive generalizable rules. Some check for the adequacy of a solution by soliciting information from the user. (Golly!)

22. Analogy in Psychology • Analogy puzzles used in intelligence tests since the very first such • tests were devised • Correlates fairly well with scores on tests of general intelligence • (0.45 - 0.82) • Four-term analogy completion task used to gauge capacity for • inductive reasoning • Miller Analogies Test (MAT) to assess scholastic aptitude at the • graduate level, and emphasizes the recognition of • verbal/conceptual semantic relations, and fine shades of • relational meaning • Annoy : Enrage :: Enlarge : (a. increase, b. exaggerate, c. augment, d. reduce).

23. Studies of mental operations in recall, recognition, RT • Artificial materials: cartoon hypothetical animals, patterns of colored squares, etc. • Pre-formulated, single format problems (four-term analogy) that are semantically-limited, and context- free. • Artificial tasks (i.e., multiple choice), multiple trials… Aha!

24. Aha! • Distinct kinds of analogizing (verb, not noun): • • Differing goals, • • Differing kinds of "given" information, • • Differing kinds of constraint, • • Differing styles of justification and criticism, and • • Differing purposes, spanning pragmatics or rhetoric, and • problem solving, • Differing kinds of sequences of operations (if one chooses to • think in terms of microcognition/causal chain theories)

25. Methods 1. Naturalism (we looked around) 2. Rationalism (we thought real hard) 3. Dumb Luck

26. A Taxonomy of “Natural Kinds” of analogy Creating analogies for use in tests, puzzles, experiments – How do people do that? Analogizing as a part of sensemaking of “the unknown” – Standard Question Analysis of pre-existing analogies in the study of comprehension, computer models, etc. Standard Question

27. A Taxonomy of “Kinds” of analogy Analytical reasoning about analogy as a concept – Try bringing that into the lab! Creating disanalogies in order to critique arguments - How do people do that? Analogizing as a continuous process - The Elevation Error

28. Ad-hoc ("to this") Analogies Reasoning with the Goal of Creating Analogies • Goal: • Construct analogies de novo, • Typically using the explicit A : B :: C : D format, • To suit particular purposes. Conjecture  Criticism  Cycle

29. Pre-hoc (“before this”) Analogy Reasoning With the Goal of Sensemaking • Occur in creative discovery contexts, as in scientific analogy. • The goal is to find coherent explanations Many models of the form: Encoding Retrieval of potential explananda Mapping (inference) e.g., Weitzenfeld-Klein model of analogical reasoning in avionics engineers

30. Pre-hoc (“before this”) Analogy • In all such models, retrieval is where the miracle happens • "The Höffding (recognition) problem" • How do you access the "right" memory, one that has explanatory potential, unless you have already accessed/retrieved it from memory? • Fishing expedition? • Not a fixed series of stages (a microcognitive view) , but a cyclo-parallelism of imagery-conjecture-criticism (a macrocognitive view)

31. Post-hoc (“after this”) Analogy Puzzle Solving of Incomplete Analogies • Post-hoc analogies are given and incomplete. • A : B : :C: __?__ • (a). D1, (b) D2, (c) D3, (d) D4 • Goal for Theorist: Develop a theory of comprehension or a computer model. • Goal for Reasoner: Discern "the" meaning of a Post-hoc analogy. • Psychological theories (e.g., Sternberg, 1977a,b) deal primarily with the Post-hoc analogy situation. • An additive method to partial out component reaction times.

32. Pro-hoc (“for this”) Analogy Reasoning With the Goal of Understanding the Concept of Analogy or Testing a Theory of Analogy • Subtle: Thinking about analogy as a concept, or analyzing theories or models of analogy. • Analogies are selected for the purpose of assessing or refining a theory or model of Post-hoc analogy. • Both the goal and the "given" information fall at what might be called a meta-level.

33. Pro-hoc (“for this”) Analogy Reasoning With the Goal of Understanding the Concept of Analogy or Testing a Theory of Analogy • Most AI models are situated in the Pro-hoc analogy context. • That is, the models first perform a Post-hoc analysis, fleshing out a given analogy, and then they conduct a Pro-hoc evaluation or justification stage. • Example: the Structure Mapping Engine (SME) (Forbus, Ferguson, and Gentner, 1994).

34. Contra-hoc (“against this”) Analogy Poking Holes in Arguments or Theories • Intended to show the limitations of an argument, including the rationale for a computational model. • Four kinds : • Rebuttal Analogy • Disanalogy • Misanalogy • Monster Analogy

35. Rebuttal Analogy • Used to persuade; a commonly-used rhetorical device. • (e.g., ways in which the recent US-Iraq war is, and is not • like the US-Vietman war) • Commentator on the US government's No Child Left Behind • education program: • “You don't fatten a pig by weighing it every day.” • Has the instrumental effect of demonstrating a flaw in the • opponent's argument • Second purpose: To show by exaggeration that the • opponent's argument is stupid and not just ridiculous

36. 2. Disanalogy In disputation, a single analogy can support contradictory or mutually exclusive conclusions. Disanalogy involves adding into an analogy one or more additional higher-order (relational) predicates, resulting in a conclusion that is contradictory to a conclusion made from the original analogy. Like rebuttal analogy, disanalogy is clever, but is perhaps more so.

37. 2. Disanalogy Goes beyond the idea that analogies are always incomplete or limited, to the idea that a single analogy can generate contradictory arguments. Models of analogy have been built on the assumption that incompatible but causally supported inferences do not follow from a single analogy. (Contra-hoc analogy in the Pro-hoc context!)

38. 2. Disanalogy Example Commentator 1: The American economy has been a strong producer for 200 years. The last thing you want to do is kill the goose that laid the golden eggs. In context, the implication was that the US should not create more regulations or “socialize” the banking system. Commentator 2: Yes, but the goose is sick and so you have to intervene somehow. In context, the implication was that some additional controls are needed.

39. 3. Misanalogy • An analogy that has been corrected in light of new information. • Example: Atoms-solar systems • As with disanalogies, misanalogies emphasize that conclusions • based on analogies may be subject to revision, as • investigators encounter new information. (Aha!)

40. 4. Monster Analogy • Analogy can involve multiple formats and a boundless variety of • semantic and conceptual relations. • Highlights the problems of creativity, “syntactic infinity” and • “semantic infinity.” • “That does not compute!”

41. 4. Monster Analogy Plato’s analogies : Philosophy :: Maxwell’s analogies : Physics

42. 4. Monster Analogy Dog : Hound :: Bother : Type Antonym : Synonym :: Opposite : Similar

43. 4. Monster Analogy • Horse : Time :: Stone: ___?_____ • King • book • girl • train

44. 4. Duplex (Monster) Analogy Field : Mouse :: Prairie : Dog Dog : Mouse :: Field : Prairie Types of rodent vs Domesticated-undomesticated

45. 4. Monster Analogy (terms can be sentences) The odorless child inspired a chocolate audience : Semantic Anomaly :: Boy book read the : Syntactic Anomaly

46. 4. Monster Analogy (terms can be sentences) This analogy : ill-formed syntax :: ill-formed semantics : Horse Because the analogy is correct in asserting its own ill-formedness, doe sit really have an anomalous semantics?

47. 4. Monster Analogy (terms can be sentences) This analogy refers to itself : Self-reference :: This analogy does not refer to itself : Contradiction (Feathers : Birds :: Hair : Mammals) : Simple :: This analogy : complex

48. Trans-hoc (“across this”) Analogy Analogical Reasoning as a Continuous Process • Actually, is probably the most common form! • (Elevation Error redux) • Rebuttal Analogy, Misanalogy, Disanalogy, and Multiple Analogy are clearly extended over time • Analogical reasoning does not always have clear “start” or “stop” (macrocog!) • Must cognitive theories end with some sort of determination that the analogy is "understood" or is “coherent?” • Must models end with the choice of a single mapping, or the evaluation of a mapping?

49. Trans-hoc (“across this”) Analogy Analogical Reasoning as a Continuous Process • Requires a rather different sort of theory from all the other forms • In addition, any of the other goal-related forms (Ad- hoc, Pro-hoc, Contra-hoc, etc.) can be manifested in the Trans-hoc context

50. Summary and Implications Would anyone expect a system for computing verbal analogies to be able to process geometrical analogies, or letter-string analogies, or analogies that mix words and geometrical forms? Modelers often claim that their systems are general, perhaps a general inference engine based on constraint satisfaction, for example. But this is based on the analysis of a single type of analogy that happens to be especially conducive to the kinds of structural analysis that are engaged