Set-theoretic completeness for epistemic and conditional logic

Authors:
Joseph Y. Halpern
Affiliations:
Department of Computer Science, Cornell University, Ithaca, NY 14853, USA E-mail: halpern@cs.cornell.edu
Venue:
Annals of Mathematics and Artificial Intelligence
Year:
1999

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Abstract

The standard approach to logic in the literature in philosophy and mathematics, which has also been adopted in computer science, is to define a language (the syntax), an appropriate class of models together with an interpretation of formulas in the language (the semantics), a collection of axioms and rules of inference characterizing reasoning (the proof theory), and then relate the proof theory to the semantics via soundness and completeness results. Here we consider an approach that is more common in the economics literature, which works purely at the semantic, set‐theoretic level. We provide set‐theoretic completeness results for a number of epistemic and conditional logics, and contrast the expressive power of the syntactic and set‐theoretic approaches.