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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Gabriele Pulcini
University of Campinas

Citations of this work

Fractional-Valued Modal Logic.Mario Piazza, Gabriele Pulcini & Matteo Tesi - 2023 - Review of Symbolic Logic 16 (4):1033-1052.
Cut elimination by unthreading.Gabriele Pulcini - 2023 - Archive for Mathematical Logic 63 (1):211-223.
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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Bridges between Classical and Nonmonotonic Logic.David Makinson - 2003 - Logic Journal of the IGPL 11 (1):69-96.

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