Fractional semantics for classical logic

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Review of Symbolic Logic 13 (4):810-828 (2020)
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Abstract

This article presents a new semantics for classical propositional logic. We begin by maximally extending the space of sequent proofs so as to admit proofs for any logical formula; then, we extract the new semantics by focusing on the axiomatic structure of proofs. In particular, the interpretation of a formula is given by the ratio between the number of identity axioms out of the total number of axioms occurring in any of its proofs. The outcome is an informational refinement of traditional Boolean semantics, obtained by breaking the symmetry between tautologies and contradictions.

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10.1017/s1755020319000431

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Citations of this work

Fractional-Valued Modal Logic.Mario Piazza, Gabriele Pulcini & Matteo Tesi - 2023 - Review of Symbolic Logic 16 (4):1033-1052.
Fractional-Valued Modal Logic and Soft Bilateralism.Mario Piazza, Gabriele Pulcini & Matteo Tesi - 2023 - Bulletin of the Section of Logic 52 (3):275-299.

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References found in this work

Introduction to mathematical logic.Alonso Church - 1958 - Revue de Métaphysique et de Morale 63 (1):118-118.
Advances in Proof-Theoretic Semantics.Peter Schroeder-Heister & Thomas Piecha (eds.) - 2015 - Cham, Switzerland: Springer Verlag.
Refutation systems in modal logic.Valentin Goranko - 1994 - Studia Logica 53 (2):299 - 324.
Bridges between Classical and Nonmonotonic Logic.David Makinson - 2003 - Logic Journal of the IGPL 11 (1):69-96.

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