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  1. Abduction as Deductive Saturation: a Proof-Theoretic Inquiry.Mario Piazza, Gabriele Pulcini & Andrea Sabatini - 2023 - Journal of Philosophical Logic 52 (6):1575-1602.
    Abductive reasoning involves finding the missing premise of an “unsaturated” deductive inference, thereby selecting a possible _explanans_ for a conclusion based on a set of previously accepted premises. In this paper, we explore abductive reasoning from a structural proof-theory perspective. We present a hybrid sequent calculus for classical propositional logic that uses sequents and antisequents to define a procedure for identifying the set of analytic hypotheses that a rational agent would be expected to select as _explanans_ when presented with an (...)
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  • Complementary Proof Nets for Classical Logic.Gabriele Pulcini & Achille C. Varzi - 2023 - Logica Universalis 17 (4):411-432.
    A complementary system for a given logic is a proof system whose theorems are exactly the formulas that are not valid according to the logic in question. This article is a contribution to the complementary proof theory of classical propositional logic. In particular, we present a complementary proof-net system, $$\textsf{CPN}$$ CPN, that is sound and complete with respect to the set of all classically invalid (one-side) sequents. We also show that cut elimination in $$\textsf{CPN}$$ CPN enjoys strong normalization along with (...)
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  • Fractional-Valued Modal Logic.Mario Piazza, Gabriele Pulcini & Matteo Tesi - 2023 - Review of Symbolic Logic 16 (4):1033-1052.
    This paper is dedicated to extending and adapting to modal logic the approach of fractional semantics to classical logic. This is a multi-valued semantics governed by pure proof-theoretic considerations, whose truth-values are the rational numbers in the closed interval $[0,1]$. Focusing on the modal logic K, the proposed methodology relies on three key components: bilateral sequent calculus, invertibility of the logical rules, and stability (proof-invariance). We show that our semantic analysis of K affords an informational refinement with respect to the (...)
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  • Cut elimination by unthreading.Gabriele Pulcini - 2023 - Archive for Mathematical Logic 63 (1):211-223.
    We provide a non-Gentzen, though fully syntactical, cut-elimination algorithm for classical propositional logic. The designed procedure is implemented on $$\textsf{GS4}$$ GS 4, the one-sided version of Kleene’s sequent system $$\textsf{G4}$$ G 4. The algorithm here proposed proves to be more ‘dexterous’ than other, more traditional, Gentzen-style techniques as the size of proofs decreases at each step of reduction. As a corollary result, we show that analyticity always guarantees minimality of the size of $$\textsf{GS4}$$ GS 4 -proofs.
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  • Fractional-Valued Modal Logic and Soft Bilateralism.Mario Piazza, Gabriele Pulcini & Matteo Tesi - 2023 - Bulletin of the Section of Logic 52 (3):275-299.
    In a recent paper, under the auspices of an unorthodox variety of bilateralism, we introduced a new kind of proof-theoretic semantics for the base modal logic \(\mathbf{K}\), whose values lie in the closed interval \([0,1]\) of rational numbers [14]. In this paper, after clarifying our conception of bilateralism – dubbed “soft bilateralism” – we generalize the fractional method to encompass extensions and weakenings of \(\mathbf{K}\). Specifically, we introduce well-behaved hypersequent calculi for the deontic logic \(\mathbf{D}\) and the non-normal modal logics (...)
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