Kripke semantics and tableaux for centered tense Nelson logic

Article

Calomino, I., Lewis-Smith, A., Pelaitay, G. and Zhao, Z. 2026. Kripke semantics and tableaux for centered tense Nelson logic. Reports on Mathematical Logic. 61.
TypeArticle
TitleKripke semantics and tableaux for centered tense Nelson logic
AuthorsCalomino, I., Lewis-Smith, A., Pelaitay, G. and Zhao, Z.
Abstract

We develop a Kripke semantics and a labelled tableau calculus for the logic of centered tense Nelson algebras. The semantics is obtained by combining the relational representation of intuitionistic tense algebras with the Kalman construction. Formulae are interpreted by pairs of disjoint upsets, recording verification and falsification; this two-component interpretation is forced by strong negation and by the negative component of Nelson implication. Using the established representation theory of IKt-algebras together with the Kalman equivalence, we connect the algebraic and relational semantics and establish soundness and completeness of the tableau calculus.

KeywordsIntuitionistic tense logic; Nelson algebra; Kalman construction; Kripke semantics; labelled tableaux
Sustainable Development Goals9 Industry, innovation and infrastructure
Middlesex University ThemeCreativity, Culture & Enterprise
Research GroupFoundations of Computing group
PublisherJagiellonian University Press
JournalReports on Mathematical Logic
ISSN0137-2904
Electronic2084-2589
Publication process dates
Accepted12 Oct 2026
Deposited13 Oct 2026
Output statusAccepted
Accepted author manuscript
File Access Level
Open
Copyright Statement

Licence: CC BY 4.0

LanguageEnglish
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