Fractional-Valued Modal Logic and Soft Bilateralism - Piazza, Mario; Pulcini, Gabriele; Tesi, Matteo (Bulletin of the Section of Logic, 2023)
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.