Fractional-Valued Modal Logic and Soft Bilateralism

Mario Piazza; Gabriele Pulcini; Matteo Tesi

doi:10.18778/0138-0680.2023.17

Authors

Mario Piazza Scuola Normale Superiore, Classe di Lettere e Filosofia
Gabriele Pulcini University of Rome “Tor Vergata”, Department of Literary, Philosophical and Art History Studies
Matteo Tesi Scuola Normale Superiore, Classe di Lettere e Filosofia

DOI:

https://doi.org/10.18778/0138-0680.2023.17

Keywords:

modal logic, general proof theory (including proof-theoretic semantics), many-valued logics

Abstract

In a recent paper, under the auspices of an unorthodox variety of bilateralism, we introduced a new kind of proof-theoretic semantics for the base modal logic \(\mathbf{K}\), whose values lie in the closed interval \([0,1]\) of rational numbers [14]. In this paper, after clarifying our conception of bilateralism – dubbed “soft bilateralism” – we generalize the fractional method to encompass extensions and weakenings of \(\mathbf{K}\). Specifically, we introduce well-behaved hypersequent calculi for the deontic logic \(\mathbf{D}\) and the non-normal modal logics \(\mathbf{E}\) and \(\mathbf{M}\) and thoroughly investigate their structural properties.

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