A Kripke semantics and tableau for monadic Wajsberg logic

Conference paper

Lewis-Smith, A. 2026. A Kripke semantics and tableau for monadic Wajsberg logic. Geatti, L. and Piazza, C. (ed.) 27th Italian Conference on Theoretical Computer Science. Udine, Italy 07 - 09 Sep 2026 CEUR Workshop Proceedings (CEUR-WS.org). pp. 1-14
TypeConference paper
TitleA Kripke semantics and tableau for monadic Wajsberg logic
AuthorsLewis-Smith, A.
Abstract

We develop a Kripke-style relational semantics and labelled tableau calculus for monadic Wajsberg logic, the implication–negation presentation of the monadic fragment of infinite-valued Łukasiewicz logic. The semantics isolates the order, involution, partial operations for Wajsberg implication, and equivalence relation arising in the dual representations of Martínez and Figallo-Orellano. The corresponding relational conditions become structural tableau rules. We prove soundness and completeness of the tableau with respect to our semantics, and obtain the finite relational countermodel property: every non-valid formula fails in a finite monadic Wajsberg model.

KeywordsŁukasiewicz logic; monadic operators; Kripke semantics; Wajsberg logic; Labelled tableau; MV algebras; finite countermodel property
Sustainable Development Goals9 Industry, innovation and infrastructure
Middlesex University ThemeCreativity, Culture & Enterprise
Conference27th Italian Conference on Theoretical Computer Science
Page range1-14
Proceedings TitleProceedings of the 27th Italian Conference on Theoretical Computer Science
EditorsGeatti, L. and Piazza, C.
ISSN1613-0073
PublisherCEUR Workshop Proceedings (CEUR-WS.org)
Copyright Year2026
Publication dates
Print19 Sep 2026
Publication process dates
Accepted29 Jul 2026
Deposited17 Aug 2026
Output statusPublished
Publisher's version
License
File Access Level
Open
Copyright Statement

© 2022 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).

Web address (URL)https://ceur-ws.org/Vol-4269/paper15.pdf
Web address (URL) of conference proceedingshttps://ceur-ws.org/Vol-4269/
LanguageEnglish
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