Effective Semantics for the Modal Logics K and KT via Non-deterministic Matrices-Reference-Cited by-同舟云学术

Effective Semantics for the Modal Logics K and KT via Non-deterministic Matrices

Published:2022 Issue: Volume: Page:468-485
ISSN:0302-9743
Container-title:Automated Reasoning
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Author:

Lahav Ori,Zohar Yoni

Abstract

AbstractA four-valued semantics for the modal logic K is introduced. Possible worlds are replaced by a hierarchy of four-valued valuations, where the valuations of the first level correspond to valuations that are legal w.r.t. a basic non-deterministic matrix, and each level further restricts its set of valuations. The semantics is proven to be effective, and to precisely capture derivations in a sequent calculus for K of a certain form. Similar results are then obtained for the modal logic KT, by simply deleting one of the truth values.

Publisher

Springer International Publishing

Link

https://link.springer.com/content/pdf/10.1007/978-3-031-10769-6_28

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