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

Ori Lahav; Yoni Zohar

doi:10.1007/978-3-031-10769-6_28

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

Ori Lahav
, Yoni Zohar

Department of Computer Science and Artificial Intelligence

Tel Aviv University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

14 Scopus citations

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 language	English
Title of host publication	Automated Reasoning - 11th International Joint Conference, IJCAR 2022, Proceedings
Editors	Jasmin Blanchette, Laura Kovács, Dirk Pattinson
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	468-485
Number of pages	18
ISBN (Print)	9783031107689
DOIs	https://doi.org/10.1007/978-3-031-10769-6_28
State	Published - 2022
Event	11th International Joint Conference on Automated Reasoning, IJCAR 2022, part of the Federated Logic Conference, FLoC 2022 - Haifa, Israel Duration: 8 Aug 2022 → 10 Aug 2022

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	13385 LNAI
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	11th International Joint Conference on Automated Reasoning, IJCAR 2022, part of the Federated Logic Conference, FLoC 2022
Country/Territory	Israel
City	Haifa
Period	8/08/22 → 10/08/22

Bibliographical note

Publisher Copyright:
© 2022, The Author(s).

Funding

We thank the anonymous reviewers for their useful feedback. This research was supported by NSF-BSF (grant number 2020704), ISF (grant numbers 619/21 and 1566/18), and the Alon Young Faculty Fellowship.

Funders	Funder number
Alon Young Faculty Fellowship
NSF-BSF	2020704
Israel Science Foundation	619/21, 1566/18

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10.1007/978-3-031-10769-6_28

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

Cite this

Lahav, O., & Zohar, Y. (2022). Effective Semantics for the Modal Logics K and KT via Non-deterministic Matrices. In J. Blanchette, L. Kovács, & D. Pattinson (Eds.), Automated Reasoning - 11th International Joint Conference, IJCAR 2022, Proceedings (pp. 468-485). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 13385 LNAI). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-10769-6_28

Lahav, Ori ; Zohar, Yoni. / Effective Semantics for the Modal Logics K and KT via Non-deterministic Matrices. Automated Reasoning - 11th International Joint Conference, IJCAR 2022, Proceedings. editor / Jasmin Blanchette ; Laura Kovács ; Dirk Pattinson. Springer Science and Business Media Deutschland GmbH, 2022. pp. 468-485 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Lahav, O & Zohar, Y 2022, Effective Semantics for the Modal Logics K and KT via Non-deterministic Matrices. in J Blanchette, L Kovács & D Pattinson (eds), Automated Reasoning - 11th International Joint Conference, IJCAR 2022, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 13385 LNAI, Springer Science and Business Media Deutschland GmbH, pp. 468-485, 11th International Joint Conference on Automated Reasoning, IJCAR 2022, part of the Federated Logic Conference, FLoC 2022, Haifa, Israel, 8/08/22. https://doi.org/10.1007/978-3-031-10769-6_28

Effective Semantics for the Modal Logics K and KT via Non-deterministic Matrices. / Lahav, Ori; Zohar, Yoni.
Automated Reasoning - 11th International Joint Conference, IJCAR 2022, Proceedings. ed. / Jasmin Blanchette; Laura Kovács; Dirk Pattinson. Springer Science and Business Media Deutschland GmbH, 2022. p. 468-485 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 13385 LNAI).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Lahav O, Zohar Y. Effective Semantics for the Modal Logics K and KT via Non-deterministic Matrices. In Blanchette J, Kovács L, Pattinson D, editors, Automated Reasoning - 11th International Joint Conference, IJCAR 2022, Proceedings. Springer Science and Business Media Deutschland GmbH. 2022. p. 468-485. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-031-10769-6_28

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

Abstract

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Bibliographical note

Funding

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