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

Gabriele Pulcini
University of Campinas
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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DOI 10.1017/s1755020319000431
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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.
A Minimal Classical Sequent Calculus Free of Structural Rules.Dominic Hughes - 2010 - Annals of Pure and Applied Logic 161 (10):1244-1253.

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