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Fractional-Valued Modal Logic and Soft Bilateralism
Bulletin of the Section of Logic, Tome 52 (2023) no. 3, pp. 275-299.

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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 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 𝐊. Specifically, we introduce well-behaved hypersequent calculi for the deontic logic 𝐃 and the non-normal modal logics 𝐄 and 𝐌 and thoroughly investigate their structural properties.
Keywords: modal logic, general proof theory (including proof-theoretic semantics), many-valued logics 
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Piazza, Mario; Pulcini, Gabriele; Tesi, Matteo. Fractional-Valued Modal Logic and Soft Bilateralism. Bulletin of the Section of Logic, Tome 52 (2023) no. 3, pp. 275-299. http://geodesic.mathdoc.fr/item/BSL_2023_52_3_a0/

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