20 found
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  1.  44
    The Implicit Commitment of Arithmetical Theories and Its Semantic Core.Carlo Nicolai & Mario Piazza - 2019 - Erkenntnis 84 (4):913-937.
    According to the implicit commitment thesis, once accepting a mathematical formal system S, one is implicitly committed to additional resources not immediately available in S. Traditionally, this thesis has been understood as entailing that, in accepting S, we are bound to accept reflection principles for S and therefore claims in the language of S that are not derivable in S itself. It has recently become clear, however, that such reading of the implicit commitment thesis cannot be compatible with well-established positions (...)
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  2.  24
    Fractional semantics for classical logic.Mario Piazza & Gabriele Pulcini - 2020 - Review of Symbolic Logic 13 (4):810-828.
    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 (...)
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  3.  20
    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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  4.  13
    Uniqueness of axiomatic extensions of cut-free classical propositional logic.Mario Piazza & Gabriele Pulcini - 2016 - Logic Journal of the IGPL 24 (5).
  5.  22
    A logic of non-monotonic interactions.Giovanni Boniolo, Marcello DʼAgostino, Mario Piazza & Gabriele Pulcini - 2013 - Journal of Applied Logic 11 (1):52-62.
  6.  71
    Adding logic to the toolbox of molecular biology.Giovanni Boniolo, Marcello D’Agostino, Mario Piazza & Gabriele Pulcini - 2015 - European Journal for Philosophy of Science 5 (3):399-417.
    The aim of this paper is to argue that logic can play an important role in the “toolbox” of molecular biology. We show how biochemical pathways, i.e., transitions from a molecular aggregate to another molecular aggregate, can be viewed as deductive processes. In particular, our logical approach to molecular biology — developed in the form of a natural deduction system — is centered on the notion of Curry-Howard isomorphism, a cornerstone in nineteenth-century proof-theory.
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  7.  26
    A logical calculus for controlled monotonicity.Marcello D'Agostino, Mario Piazza & Gabriele Pulcini - 2014 - Journal of Applied Logic 12 (4):558-569.
  8.  24
    Molecular Biology Meets Logic: Context-Sensitiveness in Focus.Giovanni Boniolo, Marcello D’Agostino, Mario Piazza & Gabriele Pulcini - 2021 - Foundations of Science 28 (1):307-325.
    Some real life processes, including molecular ones, are context-sensitive, in the sense that their outcome depends on side conditions that are most of the times difficult, or impossible, to express fully in advance. In this paper, we survey and discuss a logical account of context-sensitiveness in molecular processes, based on a kind of non-classical logic. This account also allows us to revisit the relationship between logic and philosophy of science (and philosophy of biology, in particular).
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  9.  95
    Possibilities regained: neo-Lewisian contextualism and ordinary life.Mario Piazza & Nevia Dolcini - 2020 - Synthese 197 (11):4887-4906.
    According to David Lewis, the predicate ‘knows’ is context-sensitive in the sense that its truth conditions vary across conversational contexts, which stretch or compress the domain of error possibilities to be eliminated by the subject’s evidence. Our concern in this paper is to thematize, assess, and overcome within a neo-Lewisian contextualist project two important mismatches between our use of ‘know’ in ordinary life and the use of ‘know’ by ‘Lewisian’ ordinary speakers. The first mismatch is that Lewisian contextualism still overgenerates (...)
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  10.  54
    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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  11. A Deflationary Account of the Truth of the Gödel Sentence.Gabriele Pulcini & Mario Piazza - 2014 - In Giorgio Venturi, Marco Panza & Gabriele Lolli (eds.), From Logic to Practice: Italian Studies in the Philosophy of Mathematics. Cham: Springer International Publishing.
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  12.  23
    Non-contractive logics, paradoxes, and multiplicative quantifiers.Carlo Nicolai, Mario Piazza & Matteo Tesi - forthcoming - Review of Symbolic Logic:1-21.
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  13.  21
    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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  14.  49
    Linguistic applications of first order intuitionistic linear logic.Richard Moot & Mario Piazza - 2001 - Journal of Logic, Language and Information 10 (2):211-232.
    In this paper we will discuss the first order multiplicative intuitionistic fragment of linear logic, MILL1, and its applications to linguistics. We give an embedding translation from formulas in the Lambek Calculus to formulas in MILL1 and show this translation is sound and complete. We then exploit the extra power of the first order fragment to give an account of a number of linguistic phenomena which have no satisfactory treatment in the Lambek Calculus.
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  15.  18
    What Arrow’s Information Paradox Says.Marco Pedicini & Mario Piazza - 2019 - In Matteo Vincenzo D'Alfonso & Don Berkich (eds.), On the Cognitive, Ethical, and Scientific Dimensions of Artificial Intelligence. Springer Verlag. pp. 83-94.
    Arrow’s information paradox features the most radical kind of information asymmetry by diagnosing an inherent conflict between two parties inclined to exchange information. In this paper, we argue that this paradox is more richly textured than generally supposed by current economic discussion on it and that its meaning encroaches on philosophy. In particular, we uncovers the ‘epistemic’ and more genuine version of the paradox, which looms on our cognitive lives like a sort of tax on curiosity. Finally, we sketch the (...)
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  16.  19
    Contro l'equilibrio riflessivo.Mario Piazza - 2006 - Rivista di Filosofia 97 (2):209-232.
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  17.  37
    Exchange rules.Mario Piazza - 2001 - Journal of Symbolic Logic 66 (2):509-516.
    In this paper, we show by a proof-theoretical argument that in a logic without structural rules, that is in noncommutative linear logic with exponentials, every formula A for which exchange rules (and weakening and contraction as well) are admissible is provably equivalent to ?A. This property shows that the expressive power of "noncommutative exponentials" is much more important than that of "commutative exponentials".
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  18. Erratum: Chapter 5 A Deflationary Account of the Truth of the Gödel Sentence.Gabriele Pulcini & Mario Piazza - 2014 - In Giorgio Venturi, Marco Panza & Gabriele Lolli (eds.), From Logic to Practice: Italian Studies in the Philosophy of Mathematics. Cham: Springer International Publishing.
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  19.  32
    Truth, Existence and Explanation: Filmat 2016 Studies in the Philosophy of Mathematics.Gabriele Pulcini & Mario Piazza (eds.) - 2018 - Cham, Switzerland: Springer Verlag.
    This book contains more than 15 essays that explore issues in truth, existence, and explanation. It features cutting-edge research in the philosophy of mathematics and logic. Renowned philosophers, mathematicians, and younger scholars provide an insightful contribution to the lively debate in this interdisciplinary field of inquiry. The essays look at realism vs. anti-realism as well as inflationary vs. deflationary theories of truth. The contributors also consider mathematical fictionalism, structuralism, the nature and role of axioms, constructive existence, and generality. In addition, (...)
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  20.  15
    What’s so Special About the Gödel Sentence $$\mathcal {G}$$?Gabriele Pulcini & Mario Piazza - 2016 - In Francesca Boccuni & Andrea Sereni (eds.), Objectivity, Realism, and Proof. FilMat Studies in the Philosophy of Mathematics. Cham, Switzerland: Springer International Publishing.
    The very fact that the Gödel sentence $$\mathcal {G}$$ is independent of Peano Arithmetic fuels controversy over our access to the truth of $$\mathcal {G}$$. In particular, does the truth of $$\mathcal {G}$$ $$ ) precede the truth of its numerical instances $$\varphi $$, $$\varphi $$, $$\varphi, \ldots $$, as the so-called standard argument induces one to believe? This paper offers a shift in perspective on this old problem. We start by reassessing Michael Dummett’s 1963 argument which seems to speak (...)
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