Date: 07 Nov 2001

Trade-Offs between Inductive Power and Logical Omniscience in Modeling Context

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Abstract

In a series of recent papers the economist Michael Bacharach [2] has pointed out that most approaches in knowledge representation suffer from two complementary defects. Typically they assume that agents know all the logical consequences of information encoded in a finite knowledge base (Cleverness) and only these consequences (Cloistered-ness). In this article we develop first-order and inductive extensions of Montague-Scott’s semantics in order to tackle both problems at once. Three desiderata are put forward for representing epistemic context: (1) expressive adequacy, (2) inductive power, (3) boundedness. An important part of our effort focuses on reconsidering the role of standard formalisms (both logical and probabilistic) in representing the information of bounded agents.