A Kripke semantics for commutative generalised basic logic

Conference paper

Lewis-Smith, A. and Zhao, Z. 2026. A Kripke semantics for commutative generalised basic logic. 8th Asian Workshop on Philosophical Logic . Chongqing, China 06 - 08 Apr 2026 Springer.
TypeConference paper
TitleA Kripke semantics for commutative generalised basic logic
AuthorsLewis-Smith, A. and Zhao, Z.
Abstract

We provide a generalisation of Kripke semantics for generalised Basic logic without the structural rule of weakening and ex falso quodlibet, designated \emph{commutative} $\GBLe$. We prove soundness and completeness of this system with respect to our semantics, using the earlier work of Peter Jipsen and Franco Montagna \cite{JIPSEN20101559}. This paper extends the insights of \cite{Robinson2021-LEWKSF} from $\GBLewf$ to the unbounded, weakening and contraction-free case, making for a fuzzy form of linear logic.

KeywordsSubstructural logic; fuzzy logic; Kripke Semantics; relevant Logic; linear logic; affine logic
Sustainable Development Goals9 Industry, innovation and infrastructure
Middlesex University ThemeCreativity, Culture & Enterprise
Conference8th Asian Workshop on Philosophical Logic
SeriesLogic in Asia: Studia Logica Library
PublisherSpringer
Publication process dates
Accepted05 Jan 2026
Deposited27 Jan 2026
Output statusAccepted
Accepted author manuscript
File Access Level
Open
LanguageEnglish
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