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

Ori Lahav, Yoni Zohar*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

A 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.

Original languageEnglish
Title of host publicationAutomated Reasoning - 11th International Joint Conference, IJCAR 2022, Proceedings
EditorsJasmin Blanchette, Laura Kovács, Dirk Pattinson
PublisherSpringer Science and Business Media Deutschland GmbH
Pages468-485
Number of pages18
ISBN (Print)9783031107689
DOIs
StatePublished - 2022
Event11th International Joint Conference on Automated Reasoning, IJCAR 2022, part of the Federated Logic Conference, FLoC 2022 - Haifa, Israel
Duration: 8 Aug 202210 Aug 2022

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13385 LNAI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference11th International Joint Conference on Automated Reasoning, IJCAR 2022, part of the Federated Logic Conference, FLoC 2022
Country/TerritoryIsrael
CityHaifa
Period8/08/2210/08/22

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