Local Intuitionistic Modal Logics and Their Calculi

2024/03/11 by Philippe Balbiani, Han Gao, Balbiani, Philippe +5 · 2 citations
Computer Science · #Advanced Algebra and Logic #FOS: Computer and information sciences #Logic in Computer Science (cs.LO) #Logic, Reasoning, and Knowledge

paper · pdf · doi:10.48550/arxiv.2403.06772

openalex publication_date 2024/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate intuitionistic modal logics with locally interpreted \square and \lozenge. The basic logic LIK is stronger than constructive modal logic WK and incomparable with intuitionistic modal logic IK. We propose an axiomatization of LIK and some of its extensions. We propose bi-nested calculi for LIK and these extensions, thus providing both a decision procedure and a procedure of finite countermodel extraction.

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• Intuitionistic modal logic LIK4 is decidable
• Intuitionistic modal logics: epistemic reasoning with distributed knowledge

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