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Fractional-Valued Modal Logic and Soft Bilateralism

Authors

Mario Piazza Author
Gabriele Pulcini Author
Matteo Tesi Scuola Normale Superiore di Pisa Author

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. 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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Published

2023-08-09

Versions

2023-08-16 (2)
2023-08-09 (1)

Issue

Vol. 52 No. 3 (2023): Special issue: Bilateralism and Proof-Theoretic Semantics (Part II)

Section

Research Article

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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

How to Cite

Piazza, Mario, Gabriele Pulcini, and Matteo Tesi. 2023. “Fractional-Valued Modal Logic and Soft Bilateralism”. Bulletin of the Section of Logic 52 (3): 25 pp. https://doi.org/10.18778/0138-0680.2023.17.