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FRACTIONAL SEMANTICS FOR CLASSICAL LOGIC

Published online by Cambridge University Press:  10 September 2019

MARIO PIAZZA  and
GABRIELE PULCINI
MARIO PIAZZA*
Affiliation:
Scuola Normale Superiore di Pisa
GABRIELE PULCINI*
Affiliation:
Departamento de Matemática, Universidade Nova de Lisboa
*
*SCUOLA NORMALE SUPERIORE CLASSE DI LETTERE E FILOSOFIA PISA, ITALY E-mail: mario.piazza@sns.it
†DEPARTAMENTO DE MATEMÁTICA UNIVERSIDADE NOVA DE LISBOA CAMPUS DE CAPARICA, PORTUGAL E-mail: g.pulcini@fct.unl.pt
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Abstract

This article presents a new (multivalued) 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.

Keywords

03B050374503B5003B42classical propositional logicproof theory and constructive mathematicsmany-valued logicslogics of knowledge and belief
Type
Research Article
Information
The Review of Symbolic Logic , Volume 13 , Issue 4 , December 2020 , pp. 810 - 828
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Copyright
Copyright © Association for Symbolic Logic 2019 

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