Fractional-Valued Modal Logic

Review of Symbolic Logic 16 (4):1033-1052 (2023)
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Abstract

This paper is dedicated to extending and adapting to modal logic the approach of fractional semantics to classical logic. This is a multi-valued semantics governed by pure proof-theoretic considerations, whose truth-values are the rational numbers in the closed interval $[0,1]$. Focusing on the modal logic K, the proposed methodology relies on three key components: bilateral sequent calculus, invertibility of the logical rules, and stability (proof-invariance). We show that our semantic analysis of K affords an informational refinement with respect to the standard Kripkean semantics (a new proof of Dugundji’s theorem is a case in point) and it raises the prospect of a proof-theoretic semantics for modal logic.

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Gabriele Pulcini
University of Campinas

Citations of this work

Logical Multilateralism.Heinrich Wansing & Sara Ayhan - 2023 - Journal of Philosophical Logic 52 (6):1603-1636.
Fractional-Valued Modal Logic and Soft Bilateralism.Mario Piazza, Gabriele Pulcini & Matteo Tesi - 2023 - Bulletin of the Section of Logic 52 (3):275-299.

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References found in this work

Yes and no.I. Rumfitt - 2000 - Mind 109 (436):781-823.
Proof Analysis in Modal Logic.Sara Negri - 2005 - Journal of Philosophical Logic 34 (5-6):507-544.
Advances in Proof-Theoretic Semantics.Peter Schroeder-Heister & Thomas Piecha (eds.) - 2015 - Cham, Switzerland: Springer Verlag.
A more general general proof theory.Heinrich Wansing - 2017 - Journal of Applied Logic 25:23-46.

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