Analogy

Analogy is (1) similarity in which the same relations hold between different domains or systems; (2) inference that if two things agree in certain respects then they probably agree in others. These two senses are related, as discussed below.

Analogy is important in cognitive science for several reasons. It is central in the study of LEARNING and discovery. Analogies permit transfer across different CONCEPTS, situations, or domains and are used to explain new topics. Once learned, they can serve as MENTAL MODELS for understanding a new domain (Halford 1993). For example, people often use analogies with water flow when reasoning about electricity (Gentner and Gentner 1983). Analogies are often used in PROBLEM SOLVING and inductive reasoning because they can capture significant parallels across different situations. Beyond these mundane uses, analogy is a key mechanism in CREATIVITY and scientific discovery. For example, Johannes Kepler used an analogy with light to hypothesize that the planets are moved by an invisible force from the sun. In studies of microbiology laboratories, Dunbar (1995) found that analogies are both frequent and important in the discovery process.

Analogy is also used in communication and persuasion. For example, President Bush analogized the Persian Gulf crisis to the events preceding World War II, comparing Saddam Hussein to Hitler (Spellman and Holyoak 1992). The invited inference was that the United States should defend Kuwait and Saudi Arabia against Iraq, just as the Allies defended Europe against Nazi Germany. On a larger scale, conceptual metaphors such as "weighing the evidence" and "balancing the pros and cons" can be viewed as large-scale conventionalized analogies (see COGNITIVE LINGUISTICS). Finally, analogy and its relative, SIMILARITY, are important because they participate in many other cognitive processes. For example, exemplar-based theories of conceptual structure and CASE-BASED REASONING models in artificial intelligence assume that much of human categorization and reasoning is based on analogies between the current situation and prior situations (cf. JUDGMENT HEURISTICS).

The central focus of analogy research is on the mapping process by which people understand one situation in terms of another. Current accounts distinguish the following subprocesses: mapping, that is, aligning the representational structures of the two cases and projecting inferences; and evaluation of the analogy and its inferences. These first two are signature phenomena of analogy. Two further processes that can occur are adaptation or rerepresentation of one or both analogs to improve the match and abstraction of the structure common to both analogs. We first discuss these core processes, roughly in the order in which they occur during normal processing. Then we will take up the issue of analogical retrieval, the processes by which people are spontaneously reminded of past similar or analogous examples from long-term memory.

In analogical mapping, a familiar situation -- the base or source analog -- is used as a model for making inferences about an unfamiliar situation -- the target analog. According to Gentner's structure-mapping theory (1983), the mapping process includes a structural alignment between two represented situations and the projection of inferences from one to the other. The alignment must be structurally consistent, that is, there must be a one-to-one correspondence between the mapped elements in the base and target, and the arguments of corresponding predicates must also correspond (parallel connectivity). Given this alignment, candidate inferences are drawn from the base to the target via a kind of structural completion. A further assumption is the systematicity principle: a system of relations connected by higher-order constraining relations such as causal relations is more salient in analogy than an equal number of independent matches. Systematicity links the two classic senses of analogy, for if analogical similarity is modeled as common relational structure, then a base domain that possesses a richly linked system of connected relations will yield candidate inferences by completing the connected structure in the target (Bowdle and Gentner 1997).

Another important psychological approach to analogical mapping is offered by Holyoak (1985), who emphasized the role of pragmatics in problem solving by analogy -- how current goals and context guide the interpretation of an analogy. Holyoak defined analogy as similarity with respect to a goal, and suggested that mapping processes are oriented toward attainment of goal states. Holyoak and Thagard (1989) combined this pragmatic focus with the assumption of structural consistency and developed a multiconstraint approach to analogy in which similarity, structural parallelism, and pragmatic factors interact to produce an interpretation.

Through rerepresentation or adaptation, the representation of one or both analogs is altered to improve the match. Although central to conceptual change, this aspect of analogy remains relatively unexplored. And through schema abstraction, which retains the common system representing the interpretation of an analogy for later use, analogy can promote the formation of new relational categories and abstract rules.

Evaluation is the process by which we judge the acceptability of an analogy. At least three criteria seem to be involved: structural soundness -- whether the alignment and the projected inferences are structurally consistent; factual validity of the candidate inferences -- because analogy is not a deductive mechanism, this is not guaranteed and must be checked separately; and finally, in problem-solving situations, goal-relevance -- the reasoner must ask whether the analogical inferences are also relevant to current goals. A lively arena of current research centers on exactly how and when these criteria are invoked in the analogical mapping process.

As discussed above, processing an analogy typically results in a common schema. Accounts of how cognitive simulation occurs fall into two classes: projection-first models, in which the schema is derived from the base and mapped to the target; and alignment-first models, in which the abstract schema is assumed to arise out of the analogical mapping process. Most current cognitive simulations take the latter approach. For example, the structure-mapping engine (SME) of Falkenhainer, Forbus, and Gentner (1989), when given two potential analogs, proceeds at first rather blindly, finding all possible local matches between elements of the base and target. Next it combines these into structurally consistent kernels, and finally it combines the kernels into the two or three largest and deepest matches of connected systems, which represent possible interpretations of the analogy. Based on this alignment, it projects candidate inferences -- by hypothesizing that other propositions connected to the common system in the base may also hold in the target. The analogical constraint-mapping engine (ACME) of Holyoak and Thagard (1989) uses a similar local-to-global algorithm, but differs in that it is a multiconstraint, winner-take-all connectionist system, with soft constraints of structural consistency, semantic similarity, and pragmatic bindings. Although the multiconstraint system permits a highly flexible mapping process, it often arrives at structurally inconsistent mappings, whose candidate inferences are indeterminate. Markman (1997) found that this kind of indeterminacy was rarely experienced by people solving analogies. Other variants of the local-to-global algorithm are Hofstadter and Mitchell's Copycat system (1994) for perceptual analogies and Keane's incremental analogy machine (IAM; 1990), which adds matches incrementally in order to model effects of processing order. In contrast to alignment-first models, in which inferences are made after the two representations are aligned, projection-first models find or derive an abstraction in the base and then project it to the target (e.g., Greiner 1988). Although alignment-first models are more suitable for modeling the generation of new abstractions, projection-first models may be apt for modeling conventional analogy and metaphor.

Finally, analogy has proved challenging to subsymbolic connectionist approaches. A strong case can be made that analogical processing requires structured representations and structure-sensitive processing algorithms. An interesting recent "symbolic connectionist" model, Hummel and Holyoak's LISA (1997), combines such structured symbolic techniques with distributed concept representations.

Thus far, our focus has been on how analogy is processed once it is present. But to model the use of analogy and similarity in real-life learning and reasoning we must also understand how people think of analogies; that is, how they retrieve potential analogs from long-term memory. There is considerable evidence that similarity-based retrieval is driven more by surface similarity and less by structural similarity than is the mapping process. For example, Gick and Holyoak (1980; 1983) showed that people often fail to access potentially useful analogs. People who saw an analogous story prior to being given a very difficult thought problem were three times as likely to solve the problem as those who did not (30 percent vs. 10 percent). Impressive as this is, the majority of subjects nonetheless failed to benefit from the analogy. However, when the nonsolvers were given the hint to think back to the prior story, the solution rate again tripled, to about 80-90 percent. Because no new information was given about the story, we can infer that subjects had retained its meaning, but failed to think of it when reading the problem. The similarity match between the story and the problem, though sufficient to carry out the mapping once both analogs were present in working memory, did not lead to spontaneous retrieval. This is an example of the inert knowledge problem in transfer, a central concern in EDUCATION.

Not only do people fail to retrieve analogies, but they are often reminded of prior surface-similar cases, even when they know that these matches are of little use in reasoning (Gentner, Rattermann, and Forbus 1993). This relative lack of spontaneous analogical transfer and predominance of surface remindings is seen in problem solving (Ross 1987) and may result in part from overly concrete representations (Bassok, Wu, and Olseth 1995).

Computational models of similarity-based retrieval have taken two main approaches. One class of models aims to capture the phenomena of human memory retrieval, including both strengths and weaknesses. For example, analog retrieval by constraint satisfaction (ARCS; Thagard et al. 1990) and Many are called/but few are chosen (MAC/FAC; Forbus, Gentner, and Law 1995) both assume that retrieval is strongly influenced by surface similarity and by structural similarity, goal relevance, or both. In contrast, most case-based reasoning (CBR) models aim for optimality, focusing on how to organize memory such that relevant cases are retrieved when needed.

Theories of analogy have been extended to other kinds of similarity, such as METAPHOR and mundane literal similarity. There is evidence that computing a literal similarity match involves the same process of structural alignment as does analogy (Gentner and Markman 1997). Current computational models like ACME and SME use the same processing algorithms for similarity as for analogy.

The investigation of analogy has been characterized by unusually fruitful interdisciplinary convergence. Important contributions have come from philosophy, notably Hesse's analysis (1966) of analogical models in science, and from artificial intelligence (AI), beginning with Winston's research (1982), which laid out computational strategies applicable to human processing. Recent research that combines psychological investigations and computational modeling has advanced our knowledge of how people align representational structures and compute further inferences over them. Theories of analogy and structural similarity have been successfully applied to areas such as CATEGORIZATION, DECISION MAKING, and children's learning. At the same time, cross-species comparisons have suggested that analogy may be especially well developed in human beings. These results have broadened our view of the role of structural similarity in human thought.

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-- Dedre Gentner

References

Bassok, M., L. Wu, and K. L. Olseth. (1995). Judging a book by its cover: Interpretative effects of content on problem solving transfer. Memory and Cognition 23:354-367.

Bowdle, B., and D. Gentner. (1997). Informativity and asymmetry in comparisons. Cognitive Psychology 34:244-286.

Dunbar, K. (1995). How scientists really reason: scientific reasoning in real-world laboratories. In R. J. Sternberg and J. E. Davidson, Eds., The Nature of Insight. Cambridge, MA: MIT Press, pp. 365-395.

Falkenhainer, B., K. D. Forbus, and D. Gentner. (1989). The structure-mapping engine: An algorithm and examples. Artificial Intelligence 41:1-63.

Forbus, K. D., D. Gentner, and K. Law. (1995). MAC/FAC: A model of similarity-based retrieval. Cognitive Science 19:141-205.

Gentner, D. (1983). Structure-mapping: A theoretical framework for analogy. Cognitive Science 7:155-170.

Gentner, D., and D. R. Gentner. (1983). Flowing waters or teeming crowds: Mental models of electricity. In D. Gentner and A. L. Stevens, Eds., Mental Models. Hillsdale, NJ: Erlbaum, pp. 99-129.

Gentner, D., and A. B. Markman. (1997). Structure-mapping in analogy and similarity. American Psychologist 52:45-56.

Gentner, D., M. J. Rattermann, and K. D. Forbus. (1993). The roles of similarity in transfer: Separating retrievability from inferential soundness. Cognitive Psychology 25:524-575.

Gick, M. L., and K. J. Holyoak. (1980). Analogical problem solving. Cognitive Psychology 12:306-355.

Gick, M. L., and K. J. Holyoak. (1983). Schema induction and analogical transfer. Cognitive Psychology 15:1-38.

Greiner, R. (1988). Learning by understanding analogies. Artificial Intelligence 35:81-125.

Halford, G. S. (1993). Children's Understanding: The Development of Mental Models. Hillsdale, NJ: Erlbaum.

Hesse, M. B. (1966). Models and Analogies in Science. Notre Dame, IN. University of Notre Dame Press.

Hofstadter, D. R., and M. Mitchell. (1994). The Copycat project: A model of mental fluidity and analogy-making. In K. J. Holyoak and J. A. Barnden, Eds., Advances in Connectionist and Neural Computation Theory, vol. 2, Analogical Connections. Norwood, NJ: Ablex, pp. 31-112.

Holyoak, K. J. (1985). The pragmatics of analogical transfer. In G. H. Bower, Ed., The Psychology of Learning and Motivation, vol. 19. New York: Academic Press, pp. 59-87.

Holyoak, K. J., and P. R. Thagard. (1989). Analogical mapping by constraint satisfaction. Cognitive Science 13:295-355.

Hummel, J. E., and K. J. Holyoak. (1997). Distributed representations of structure: A theory of analogical access and mapping. Psychological Review 104:427-466.

Keane, M. T. (1990). Incremental analogising: Theory and model. In K. J. Gilhooly, M. T. G. Keane, R. H. Logie, and G. Erdos, Eds., Lines of Thinking, vol. 1. Chichester, England: Wiley.

Markman, A. B. (1997). Constraints on analogical inference. Cognitive Science 21(4):373-418.

Ross, B. H. (1987). This is like that: The use of earlier problems and the separation of similarity effects. Journal of Experimental Psychology: Learning, Memory, and Cognition 13:629-639.

Spellman, B. A., and K. J. Holyoak. (1992). If Saddam is Hitler then who is George Bush? Analogical mapping between systems of social roles. Journal of Personality and Social Psychology 62:913-933.

Thagard, P., K. J. Holyoak, G. Nelson, and D. Gochfeld. (1990). Analog retrieval by constraint satisfaction. Artificial Intelligence 46:259-310.

Winston, P. H. (1982). Learning new principles from precedents and exercises. Artificial Intelligence 19:321-350.

Analogy

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