Work

A Sound and Complete Axiomatisation for Intuitionistic Linear Temporal Logic

Year: 2024

Type: conference-paper

Abstract: Intuitionistic linear temporal logic (iLTL) has been studied extensively, especially in the last decade. It enjoys natural semantics over intuitionistic Kripke frames equipped with an order-preserving function representing the temporal dynamics, known as 'expanding models'. This leads to a logic that is known to be decidable but whose axiomatisation has long remained open. We propose an extension of iLTL with the co-implication connective of Hilbert–Brouwer logic and call it 'bi-intuitionistic linear temporal logic' (biLTL). We establish that this extension is still decidable for the class of expanding models. We moreover give a sound and complete Hilbert-style calculus for it, the first for any logic extending iLTL. As a corollary, the topological semantics for intuitionistic propositional logic cannot be extended to a topological semantics for Hilbert-Brouwer logic, which thus establishes co-implication as a distinctive feature of the Kripke semantics for bi-intuitionistic logic.

DOI: 10.24963/kr.2024/33

Authors: David Fernández-Duque, Brett McLean, Lukas Zenger

Institutions: Universitat de Barcelona, Ghent University, University of Bern

Language: English

Topic: Advanced Algebra and Logic

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Funders: Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung, Fonds Wetenschappelijk Onderzoek

Awards: Proof and Model Theory of Intuitionistic Temporal Logic, G5799696092, Proof and Model Theory of Intuitionistic Temporal Logic

OpenAlex ID: W4403792790