Analogy and Representing Knowledge

badanalogiesimagesAccording to Keith Holyoak, the most important influence on analogy research in the cognitive-science tradition has been concerned with the representation of knowledge within computational systems. Holyoak credits philosopher Mary Hesse, who was in turn influenced by Aristotle’s discussions of analogy in scientific classification and Black’s  interactionist view of metaphor. Hesse placed great stress on the purpose of analogy as a tool for scientific discovery and conceptual change, and on the close connections between causal relations and analogical mapping. In the 1970s, work in artificial intelligence and psychology focused on the representation of complex knowledge of the sort used in scientific reasoning, problem solving, story comprehension, and other tasks that require structured knowledge. A key aspect of structured knowledge is that elements can be flexibly bound into the roles of relations. For example, “dog bit man” and “man bit dog” have the same elements and the same relation, but the role bindings have been reversed, radically altering the overall meaning. How the mind and brain accomplish role binding is thus a central problem to be solved by any psychological theory that involves structured knowledge, including any theory of analogy.

In the 1980s, a number of cognitive scientists recognized the centrality of analogy as a tool for discovery, as well as its close connection with theories of knowledge representation. Winston, guided by Minsky’s  treatment of knowledge representation, built a computer model of analogy that highlighted the importance of causal relations in guiding analogical inference. Other researchers in artificial intelligence also began to consider the use of complex analogies in reasoning and learning, leading to an approach to artificial intelligence termed case-based reasoning.

Meanwhile, cognitive psychologists began to consider analogy in relation to knowledge representation and eventually to integrate computational modeling with detailed experimental studies of human analogical reasoning. Gentner investigated the role of analogy in understanding scientific topics. She emphasized that in analogy, the key similarities involve relations that hold within the domains (e.g., the flow of electrons in an electrical circuit is analogically similar to the flow of people in a crowded subway tunnel), rather than in features of individual objects (e.g., electrons do not resemble people). Moreover, analogical similarities often depend on higher order relations—relations between relations. For example, adding a resistor to a circuit causes a decrease in flow of electricity, just as adding a narrow gate in the subway tunnel would decrease the rate at which people pass through (where causes is a higher order relation). In her structure-mapping theory, Gentner proposed that analogy entails finding a structural alignment, or mapping, between elements of the two domains. In this theory, a “good” alignment between two representational structures is characterized by a high degree of structural parallelism (consistent, one-to one correspondences between mapped elements)
and of systematicity—an implicit preference for deep, interconnected systems of relations governed by higher order relations, such as causal, mathematical, or other functional relations.

Holyoak and his colleagues focused on the role of analogy in problem solving, with a strong concern for the role of pragmatics in analogy—how causal relations that impact current goals and context guide the interpretation of an analogy. Holyoak and Thagard developed an approach to analogy in which several factors were viewed as jointly constraining analogical reasoning. According to their multiconstraint theory, people implicitly favor mappings that maximize structural parallelism, but that also maximize direct similarity of corresponding elements and relations, and that give priority to pragmatically important elements (i.e., those functionally related to achieving a goal). The theory further specified how the joint influence of these constraints, which often converge but sometimes conflict, might be adjudicated by a process of constraint satisfaction.  This certainly points to Holyoak being one of the originators of parallel constraint satisfaction theory.

From the perspective of Holyoak and Thagard’s multiconstraint theory, the centrality of functional structure is a basic pragmatic constraint. Causal relations constitute the prime example of “higher order” relations involved in Gentner’s systematicity constraint, which has been supported by experimental evidence that analogical transfer is more robust when the source includes causal structure than when it does not. In general, a highly systematic source will be rich in functional structure. A high degree of structural parallelism (that is, a consistent mapping between relevant elements of the source and target) is a logical requirement if the structure of the source is to provide an appropriate model for the structure of the target. Ambiguity will be minimized if the mapping is both consistent and one to one.

Holyoak and Thagard’s constraint of semantic similarity—a preference for mappings in which similar objects are placed into correspondence—also follows from the overarching goal of seeking true and goal-relevant inferences. Direct semantic  similarity of elements has often been termed “surface” similarity, in contrast to the “structural” variety. In fact, this contrast has been defined in two distinct ways in the analogy literature, indicating resemblances based either (1) on features versus relations or (2) on functionally irrelevant versus. In general, functional structure (the latter sense) will involve not only relations, but also those additional elements that participate in functional relations. For example, because an orange is round, fairly small, and firm (properties usually considered to be perceptual features, not relations), it could be considered analogous to a ball for purposes of playing catch. In this example, as in most simple empirical analogies, various perceptual properties participate in relevant causal relations and hence count as “structural” by the functional definition.

In general, objects that share direct similarities are likely to have similar causal properties. Thus, while “distant” analogies between remote domains of knowledge may be especially creative,
“close” analogies in which similar entities fill corresponding roles typically provide stronger support for plausible inferences.

Holyoak, K. J. (2012). Analogy and relational reasoning.  In K. J. Holyoak & R. G. Morrison (eds.).  The Oxford handbook of thinking and reasoning (pp 234-259).  New York: Oxford University Press.


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