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arXiv · 2507.06834

Base-extension Semantics for Intuitionistic Modal Logics

Yll Buzoku·David. J. Pym
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Abstract

The proof theory and semantics of intuitionistic modal logics have been studied by Simpson in terms of Prawitz-style labelled natural deduction systems and Kripke models. An alternative to model-theoretic semantics is provided by proof-theoretic semantics, which is a logical realization of inferentialism, in which the meaning of constructs is understood through their use. The key idea in proof-theoretic semantics is that of a base of atomic rules, all of which refer only to propositional atoms and involve no logical connectives. A specific form of proof-theoretic semantics, known as base-extension semantics (B-eS), is concerned with the validity of formulae and provides a direct counterpart to Kripke models that is grounded in the provability of atomic formulae in a base. We establish, systematically, B-eS for Simpson's intuitionistic modal logics and, also systematically, obtain soundness and completeness theorems with respect to Simpson's natural deduction systems.

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Yll Buzoku, David. J. Pym. 2025-07-09. Base-extension Semantics for Intuitionistic Modal Logics. https://arxiv.org/abs/2507.06834

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