Set-Theoretic Completeness for Epistemic and Conditional Logic

Details Set-Theoretic Completeness for Epistemic and Conditional Logic Set-Theoretic Completeness for Epistemic and Conditional Logic

1998-08-28

arxiv.org/abs/cs/9808006v2

Annals of Mathematics and Artificial Intelligence, vol. 26, 1999, pp. 1-27

Computer Science

Artificial Intelligence

This is an expanded version of a paper that appeared in AI and Mathematics, 1998

Scientific paper

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

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