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arXiv · 2309.06309

A Natural Intuitionistic Modal Logic: Axiomatization and Bi-nested Calculus

Philippe Balbiani·Han Gao·Çiğdem Gencer·Nicola Olivetti
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Abstract

We introduce FIK, a natural intuitionistic modal logic specified by Kripke models satisfying the condition of forward confluence. We give a complete Hilbert-style axiomatization of this logic and propose a bi-nested calculus for it. The calculus provides a decision procedure as well as a countermodel extraction: from any failed derivation of a given formula, we obtain by the calculus a finite countermodel of it.

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Philippe Balbiani, Han Gao, Çiğdem Gencer, Nicola Olivetti. 2023-09-12. A Natural Intuitionistic Modal Logic: Axiomatization and Bi-nested Calculus. https://arxiv.org/abs/2309.06309

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