Determination, Uniformity, and Relevance: Normative Criteria for Generalization and Reasoning by Analogy
ANALOGICAL REASONING: PERSPECTIVES OF ARTIFICIAL INTELLIGENCE, COGNITIVE SCIENCE, AND PHILOSOPHY, pp. 227-250, David H. Helman, ed., Kluwer Academic Publishers, 1988
27 Pages Posted: 12 Feb 2013 Last revised: 11 Mar 2013
Date Written: May 4, 1988
This paper defines the form of prior knowledge that is required for sound inferences by analogy and single-instance generalizations, in both logical and probabilistic reasoning. In the logical case, the first order determination rule defined in Davies (1985) is shown to solve both the justification and non-redundancy problems for analogical inference. The statistical analogue of determination that is put forward is termed 'uniformity'. Based on the semantics of determination and uniformity, a third notion of "relevance" is defined, both logically and probabilistically. The statistical relevance of one function in determining another is put forward as a way of defining the value of information: The statistical relevance of a function F to a function G is the absolute value of the change in one's information about the value of G afforded by specifying the value of F. This theory provides normative justifications for conclusions projected by analogy from one case to another, and for generalization from an instance to a rule. The soundness of such conclusions, in either the logical or the probabilistic case, can be identified with the extent to which the corresponding criteria (determination and uniformity) actually hold for the features being related.
Keywords: determination rules, analogical reasoning, generalization, relevance, uniformity, value of information, learning
JEL Classification: D83, C11, C40
Suggested Citation: Suggested Citation