Fractional semantics provides a multi-valued interpretation of a variety of logics, governed by purely proof-theoretic principles. This approach employs a method of systematic decomposition of formulas through a well-disciplined sequent calculus, assigning a fractional value that measures the “quantity of identity” (intuitively, “quantity of truth”) within a sequent. A key consequence of this framework is the breakdown of the traditional symmetry between truth and contradiction. In this paper, we explore the ramifications of this novel perspective on classical logic. Specifically, we (i) introduce an alternative paraconsistent consequence relation, and (ii) show how the gradual character of contradictions induces a corresponding characterization of tautologies, thereby obtaining a full-fledged informational refinement of classical logic.

Inside Classical Logic: Truth, Contradictions, Fractionality

Piazza, Mario
;
Tesi, Matteo
2025

Abstract

Fractional semantics provides a multi-valued interpretation of a variety of logics, governed by purely proof-theoretic principles. This approach employs a method of systematic decomposition of formulas through a well-disciplined sequent calculus, assigning a fractional value that measures the “quantity of identity” (intuitively, “quantity of truth”) within a sequent. A key consequence of this framework is the breakdown of the traditional symmetry between truth and contradiction. In this paper, we explore the ramifications of this novel perspective on classical logic. Specifically, we (i) introduce an alternative paraconsistent consequence relation, and (ii) show how the gradual character of contradictions induces a corresponding characterization of tautologies, thereby obtaining a full-fledged informational refinement of classical logic.
2025
Settore M-FIL/02 - Logica e Filosofia della Scienza
Settore PHIL-02/A - Logica e filosofia della scienza
Classical logic; Proof theory; Paraconsistency; Contradictions
   MIUR PRIN Project “Proof and Understanding in Mathematics (PUMa). Purity of methods, simplicity, and explanation in mathematical reasoning”
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/151543
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