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. 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.

Fractional-valued modal logic and soft bilateralism

Piazza Mario;Tesi Matteo
2023

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 K, whose values lie in the closed interval [0, 1] of rational numbers. 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.
2023
Settore M-FIL/02 - Logica e Filosofia della Scienza
Modal logic 03B45; proof theory, general (including proof-theoretic 16 semantics) 03F03; many-valued logics 03B50.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/128824
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