A Naturalistic Exploration of theForms and Functions of Analogizing

Robert R. HoffmanThomas K. Eskridge

Institute for Human and Machine Cognition

Cameron ShellyDalhousie University

The 9th bi-annual International Conference Naturalistic Decision Making

London 23-26 June, 2009

Outline

Examples + History and Importance of the Concept

Analogy in Computer Science

Analogy in Psychology

A Taxonomy of Kinds

Implications + Innuendos

1 : 2 :: 2 : 4

Circle : Sphere :: Triangle : Cone

Analogosgeometric or numerical proportions, ratios, or symmetries.

ATOMS ARE LIKE SOLAR SYSTEMS

SUN - NUCLEUSPLANETS - ELECTRONSORBITS - ORBITS

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.).

Analogy in science

Scream : Screams : Screaming : Screamer : Screamed :: Dream : Dreams : Dreaming : Dreamer : Dreamed

Middle AgesGrammarians – analogy as an explanation of historical change of word forms and inflections

JULIET IS LIKE THE SUN

LARGE AND MADE PRIMARILY OF GAS?

POETICS

A WOMAN WITHOUT A MAN IS LIKE

A FISH WITHOUT A BICYCLE

Middle AgesRhetoricians – analogy on par with syllogism, a form of proper argumentation

ROBIN : BIRD:: MUSTANG : ____?_____

ROBIN : BIRD:: MUSTANG : ____?_____

A.EUCARYOTEB.VERTEBRATEC.CHRONOCYCLELOGRAPHD.MENTAL TEST

Analogy as a critical process in perception, language, learning, and problem solving

OR

Analogy as a “basic,” “fundamental,” or “irreducible” mental operation

??????

One Giant Leap for Mankind

"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).

"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).

"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).

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."

Resemblance Theory

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

Analogy and Computer Science

• 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 orfiltering.

• Some process of restructuring of relations. • A distinction between features and relations.

e.g., atom-solar system example

Nearly all computational models:

Representational Techniques

Production rules

Symbolic-connectionst hybrids

Bayes nets, etc.

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.

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!)

Processing Approaches

• 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 ofrelational meaning

Annoy : Enrage :: Enlarge : (a. increase, b. exaggerate, c. augment, d. reduce).

Analogy in Psychology

• 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…

Studies of mental operations in recall, recognition, RT

Aha!

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)

1. Naturalism (we looked around)

2. Rationalism (we thought real hard)

3. Dumb Luck

Methods

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

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

Goal:

• Construct analogies de novo,

• Typically using the explicit A : B :: C : D format,

• To suit particular purposes.

Reasoning with the Goal of Creating Analogies

Ad-hoc ("to this") Analogies

Conjecture Criticism Cycle

• Occur in creative discovery contexts, as in scientific analogy.

• The goal is to find coherent explanations

Reasoning With the Goal of Sensemaking

Pre-hoc (“before this”) Analogy

Many models of the form:

Encoding

Retrieval of potential explananda

Mapping (inference)

e.g., Weitzenfeld-Klein model of analogical reasoning in avionics engineers

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)

• 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.

Puzzle Solving of Incomplete Analogies

Post-hoc (“after this”) 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.

Reasoning With the Goal of Understanding the Concept of Analogy or Testing a Theory of Analogy

Pro-hoc (“for this”) 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).

Pro-hoc (“for this”) Analogy

Reasoning With the Goal of Understanding the Concept of Analogy or Testing a Theory of Analogy

Poking Holes in Arguments or Theories

Contra-hoc (“against this”) Analogy

• Intended to show the limitations of an argument, including the rationale for a computational model.

• Four kinds :

1. Rebuttal Analogy

2. Disanalogy

3. Misanalogy

4. Monster Analogy

1. 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

2. Disanalogy

In disputation, a single analogy can support contradictory or mutually exclusive conclusions.

Disanalogy involves adding into an analogy one or more additionalhigher-order (relational) predicates, resulting in a conclusion that is contradictory to a conclusion made from the originalanalogy.

Like rebuttal analogy, disanalogy is clever, but is perhaps more so.

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!)

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.

3. Misanalogy

• An analogy that has been corrected in light of new information.

Example: Atoms-solar systems

• As with disanalogies, misanalogies emphasize that conclusionsbased on analogies may be subject to revision, as investigators encounter new information. (Aha!)

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!”

4. Monster Analogy

Plato’s analogies : Philosophy :: Maxwell’s analogies : Physics

4. Monster Analogy

Dog : Hound :: Bother : Type

Antonym : Synonym :: Opposite : Similar

4. Monster Analogy

Horse : Time :: Stone: ___?_____

a.Kingb.bookc.girld.train

4. Duplex (Monster) Analogy

Field : Mouse :: Prairie : Dog

Dog : Mouse :: Field : Prairie

Types of rodent vs Domesticated-undomesticated

4. Monster Analogy (terms can be sentences)

The odorless child inspired a chocolate audience : Semantic Anomaly ::

Boy book read the : Syntactic Anomaly

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?

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

• 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?

Analogical Reasoning as a Continuous Process

Trans-hoc (“across this”) Analogy

• 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

Analogical Reasoning as a Continuous Process

Trans-hoc (“across this”) Analogy

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, perhapsa 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

Distinct kinds of analogizing mandate differing treatments in psycholinguistics, sociolinguistics, and computational modeling, since they involve:

• 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/stage theories

Summary and Implications

What is the evidence for the assertion that analogy is a singular and fundamental mental operation?

One that is innate or universal ?

Summary and Implications

The fact that the standard analogy format can be used to give meaningful and symbolic descriptions of comparisons is not sufficient to support the claims that:

(1). Analogy is a covering term for all types of comparison, including similarity,

(2). Those relations that the theorist has described bear a necessary resemblance to the relations or ideas someone else might experience, or that

(3). A special process called analogical transfer underlies problem solving in general.

Summary and Implications

Theories of analogy, laboratory research paradigms, and computational models are based on the notion that analogy is based on this one relation -- similarity

"Similarity is a process that itself is a fundamental cognitive function"

(Medin, Goldstone, and Gentner, 1993, p.275).

There's More to it Than Similarity

Summary and Implications

Given that analogy (especially the four-term analogy used in mental tests) has become ingrained in Western civilization, it is now possible to claim that analogy is necessary for problem solving precisely because the concept of analogy and the analogy format were invented to label and describe exactly the sorts of phenomena that problem solving involves.

The Reification of Analogy

Summary and Implications

Reasoning by analogy of any Kind is a skill acquired through practice and experience.

For most of us, it is experience with Pro-hoc analogy puzzles, typically the sorts that appear in pedagogical and assessment contexts.

For some of us, it is experience in professional work (e.g., avionics)

Summary and Implications

The Mysteries of Macrocognition

• The apperception of resemblances and distinctions,

• The ability to create well-defined or analytical formats for laying out propositions that express meanings and perceptions,

• Mental imagery,

• Metaphor,

• Semantic flexibility, and

• Inference constraint

The Mysteries of Macrocognition

In general, AI models and psychological theories have as their goal the Post-hoc analysis (i.e., “build me a theory”) of incomplete Ad-hoc or Pre-hoc (i.e., pre-formulated) verbal analogies so as to generate "solutions"—single candidate completions (literal paraphrases) that satisfy certain Pre-hoc (explanatory) and Pro-hoc (i.e., justification) criteria.

Broadening the scope of research, theory, and modeling beyond that situation may be helpful as cognitive science and AI grapple with the mysteries of macrocognition—mysteries that not only seem to be the underpinnings of so-called analogical reasoning, but also mysteries for artificial intelligence.

www.ihmc.us

Thank you!