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Luca Tranchini
Universität Tübingen
  1.  18
    Proof-Theoretic Harmony: Towards an Intensional Account.Luca Tranchini - forthcoming - Synthese:1-32.
    In this paper we argue that an account of proof-theoretic harmony based on reductions and expansions delivers an inferentialist picture of meaning which should be regarded as intensional, as opposed to other approaches to harmony that will be dubbed extensional. We show how the intensional account applies to any connective whose rules obey the inversion principle first proposed by Prawitz and Schroeder-Heister. In particular, by improving previous formulations of expansions, we solve a problem with quantum-disjunction first posed by Dummett. As (...)
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  2.  6
    Ekman’s Paradox.Peter Schroeder-Heister & Luca Tranchini - 2017 - Notre Dame Journal of Formal Logic 58 (4):567-581.
    Prawitz observed that Russell’s paradox in naive set theory yields a derivation of absurdity whose reduction sequence loops. Building on this observation, and based on numerous examples, Tennant claimed that this looping feature, or more generally, the fact that derivations of absurdity do not normalize, is characteristic of the paradoxes. Striking results by Ekman show that looping reduction sequences are already obtained in minimal propositional logic, when certain reduction steps, which are prima facie plausible, are considered in addition to the (...)
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  3.  13
    The Naturality of Natural Deduction.Luca Tranchini, Paolo Pistone & Mattia Petrolo - forthcoming - Studia Logica:1-37.
    Developing a suggestion by Russell, Prawitz showed how the usual natural deduction inference rules for disjunction, conjunction and absurdity can be derived using those for implication and the second order quantifier in propositional intuitionistic second order logic NI \. It is however well known that the translation does not preserve the relations of identity among derivations induced by the permutative conversions and immediate expansions for the definable connectives, at least when the equational theory of NI \ is assumed to consist (...)
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  4.  39
    Natural Deduction for Dual-Intuitionistic Logic.Luca Tranchini - 2012 - Studia Logica 100 (3):631-648.
    We present a natural deduction system for dual-intuitionistic logic. Its distinctive feature is that it is a single-premise multiple-conclusions system. Its relationships with the natural deduction systems for intuitionistic and classical logic are discussed.
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  5.  12
    Proof, Meaning and Paradox: Some Remarks.Luca Tranchini - forthcoming - Topoi:1-13.
    In the present paper, the Fregean conception of proof-theoretic semantics that I developed elsewhere will be revised so as to better reflect the different roles played by open and closed derivations. I will argue that such a conception can deliver a semantic analysis of languages containing paradoxical expressions provided some of its basic tenets are liberalized. In particular, the notion of function underlying the Brouwer–Heyting–Kolmogorov explanation of implication should be understood as admitting functions to be partial. As argued in previous (...)
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  6.  22
    Natural Deduction for Bi-Intuitionistic Logic.Luca Tranchini - 2017 - Journal of Applied Logic 25:S72-S96.
    We present a multiple-assumption multiple-conclusion system for bi-intuitionistic logic. Derivations in the systems are graphs whose edges are labelled by formulas and whose nodes are labelled by rules. We show how to embed both the standard intuitionistic and dual-intuitionistic natural deduction systems into the proposed system. Soundness and completeness are established using translations with more traditional sequent calculi for bi-intuitionistic logic.
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  7.  12
    Proof-Theoretic Semantics, Paradoxes and the Distinction Between Sense and Denotation.Luca Tranchini - forthcoming - Journal of Logic and Computation 2014.
    In this paper we show how Dummett-Prawitz-style proof-theoretic semantics has to be modified in order to cope with paradoxical phenomena. It will turn out that one of its basic tenets has to be given up, namely the definition of the correctness of an inference as validity preservation. As a result, the notions of an argument being valid and of an argument being constituted by correct inference rules will no more coincide. The gap between the two notions is accounted for by (...)
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  8.  5
    Harmonising Harmony.Luca Tranchini - 2015 - Review of Symbolic Logic 8 (3):411-423.
  9.  2
    How to Ekman a Crabbé-Tennant.Peter Schroeder-Heister & Luca Tranchini - forthcoming - Synthese:1-23.
    Developing early results of Prawitz, Tennant proposed a criterion for an expression to count as a paradox in the framework of Gentzen’s natural deduction: paradoxical expressions give rise to non-normalizing derivations. Two distinct kinds of cases, going back to Crabbé and Tennant, show that the criterion overgenerates, that is, there are derivations which are intuitively non-paradoxical but which fail to normalize. Tennant’s proposed solution consists in reformulating natural deduction elimination rules in general form. Developing intuitions of Ekman we show that (...)
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  10.  53
    Truth From a Proof-Theoretic Perspective.Luca Tranchini - 2012 - Topoi 31 (1):47-57.
    Validity, the central concept of the so-called ‘proof-theoretic semantics’ is described as correctly applying to the arguments that denote proofs. In terms of validity, I propose an anti-realist characterization of the notions of truth and correct assertion, at the core of which is the idea that valid arguments may fail to be recognized as such. The proposed account is compared with Dummett’s and Prawitz’s views on the matter.
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  11.  11
    Stabilizing Quantum Disjunction.Luca Tranchini - 2018 - Journal of Philosophical Logic 47 (6):1029-1047.
    Since the appearance of Prior’s tonk, inferentialists tried to formulate conditions that a collection of inference rules for a logical constant has to satisfy in order to succeed in conferring an acceptable meaning to it. Dummett proposed a pair of conditions, dubbed ‘harmony’ and ‘stability’ that have been cashed out in terms of the existence of certain transformations on natural deduction derivations called reductions and expansions. A long standing open problem for this proposal is posed by quantum disjunction: although its (...)
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  12.  66
    Supervaluationism: Truth, Value and Degree Functionality.Pablo Cobreros & Luca Tranchini - 2014 - Thought: A Journal of Philosophy 3 (2):136-144.
    This article deals with supervaluationism and the failure of truth-functionality. It draws some distinctions that may contribute to a better understanding of this semantic framework.
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  13.  12
    Proof and Truth. An Anti-Realist Perspective.Luca Tranchini - unknown
    In the first chapter, we discuss Dummett’s idea that the notion of truth arises from the one of the correctness of an assertion. We argue that, in a first-order language, the need of defining truth in terms of the notion of satisfaction, which is yielded by the presence of quantifiers, is structurally analogous to the need of a notion of truth as distinct from the one of correctness of an assertion. In the light of the analogy between predicates in Frege (...)
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  14.  41
    Anti-Realistic Notions of Truth.Luca Tranchini - 2012 - Topoi 31 (1):5-8.
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  15.  6
    Truth: An Anti-Realist Adequacy Condition.Luca Tranchini - 2010 - In Piotr Stalmaszczyk (ed.), Philosophy of Language and Linguistics. Ontos Verlag. pp. 347.
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