Approximations of modal logics: image and beyond

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Annals of Pure and Applied Logic 152 (1-3):161-173 (2008)
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Abstract

Inspired by the recent work on approximations of classical logic, we present a method that approximates several modal logics in a modular way. Our starting point is the limitation of the n-degree of introspection that is allowed, thus generating modaln-logics. The semantics for n-logics is presented, in which formulas are evaluated with respect to paths, and not possible worlds. A tableau-based proof system is presented, n-SST, and soundness and completeness is shown for the approximation of modal logics image and image.

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10.1016/j.apal.2007.11.009

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