A Logical Approach to Reasoning by Analogy

In John P. McDermott (Editor), Proceedings of the Tenth International Joint Conference on Artificial Intelligence (IJCAI-87) (Milan, August 23–28), Morgan Kaufmann Publishers, Inc., 1987, pp. 264–270

7 Pages Posted: 21 Feb 2013

See all articles by Todd Davies

Todd Davies

Stanford University - Symbolic Systems Program; Center for the Study of Language and Information

Stuart Russell

University of California, Berkeley

Date Written: July 15, 1987

Abstract

We analyze the logical form of the domain knowledge that grounds analogical inferences and generalizations from a single instance. The form of the assumptions which justify analogies is given schematically as the “determination rule”, so called because it expresses the relation of one set of variables determining the values of another set. The determination relation is a logical generalization of the different types of dependency relations defined in database theory. Specifically, we define determination as a relation between schemata of first order logic that have two kinds of free variables: (1) object variables and (2) what we call “polar” variables, which hold the place of truth values. Determination rules facilitate sound rule inference and valid conclusions projected by analogy from single instances, without implying what the conclusion should be prior to an inspection of the instance. They also provide a way to specify what information is sufficiently relevant to decide a question, prior to knowledge of the answer to the question.

Keywords: analogical reasoning, determination rules, generalization, single instance induction, learning, first order logic

JEL Classification: D83

Suggested Citation

Davies, Todd R. and Russell, Stuart, A Logical Approach to Reasoning by Analogy (July 15, 1987). In John P. McDermott (Editor), Proceedings of the Tenth International Joint Conference on Artificial Intelligence (IJCAI-87) (Milan, August 23–28), Morgan Kaufmann Publishers, Inc., 1987, pp. 264–270, Available at SSRN: https://ssrn.com/abstract=2221719

Todd R. Davies (Contact Author)

Stanford University - Symbolic Systems Program ( email )

Stanford, CA 94305-2150
United States

HOME PAGE: http://www.stanford.edu/~davies

Center for the Study of Language and Information ( email )

Stanford, CA 94305-4115
United States

Stuart Russell

University of California, Berkeley ( email )

Berkeley, CA 94720-1712
United States

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