8 found
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  1. The Church–Fitch Knowability Paradox in the Light of Structural Proof Theory.Paolo Maffezioli, Alberto Naibo & Sara Negri - 2012 - Synthese 190 (14):2677-2716.
    Anti-realist epistemic conceptions of truth imply what is called the knowability principle: All truths are possibly known. The principle can be formalized in a bimodal propositional logic, with an alethic modality ${\diamondsuit}$ and an epistemic modality ${\mathcal{K}}$, by the axiom scheme ${A \supset \diamondsuit \mathcal{K} A}$. The use of classical logic and minimal assumptions about the two modalities lead to the paradoxical conclusion that all truths are known, ${A \supset \mathcal{K} A}$. A Gentzen-style reconstruction of the Church–Fitch paradox is presented (...)
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  2.  85
    Are Uniqueness and Deducibility of Identicals the Same?Alberto Naibo & Mattia Petrolo - 2015 - Theoria 81 (2):143-181.
    A comparison is given between two conditions used to define logical constants: Belnap's uniqueness and Hacking's deducibility of identicals. It is shown that, in spite of some surface similarities, there is a deep difference between them. On the one hand, deducibility of identicals turns out to be a weaker and less demanding condition than uniqueness. On the other hand, deducibility of identicals is shown to be more faithful to the inferentialist perspective, permitting definition of genuinely proof-theoretical concepts. This kind of (...)
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  3. On the Computational Meaning of Axioms.Alberto Naibo, Mattia Petrolo & Thomas Seiller - 2016 - In Ángel Nepomuceno Fernández, Olga Pombo Martins & Juan Redmond (eds.), Epistemology, Knowledge and the Impact of Interaction. Springer Verlag.
    An anti-realist theory of meaning suitable for both logical and proper axioms is investigated. As opposed to other anti-realist accounts, like Dummett-Prawitz verificationism, the standard framework of classical logic is not called into question. In particular, semantical features are not limited solely to inferential ones, but also computational aspects play an essential role in the process of determination of meaning. In order to deal with such computational aspects, a relaxation of syntax is shown to be necessary. This leads to a (...)
     
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  4.  18
    Postponement of $$Mathsf {}$$ and Glivenko’s Theorem, Revisited.Giulio Guerrieri & Alberto Naibo - 2019 - Studia Logica 107 (1):109-144.
    We study how to postpone the application of the reductio ad absurdum rule ) in classical natural deduction. This technique is connected with two normalization strategies for classical logic, due to Prawitz and Seldin, respectively. We introduce a variant of Seldin’s strategy for the postponement of \, which induces a negative translation from classical to intuitionistic and minimal logic. Through this translation, Glivenko’s theorem from classical to intuitionistic and minimal logic is proven.
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  5.  24
    Postponement of Reduction Ad Absurdum and Glivenko’s Theorem, Revisited.Giulio Guerrieri & Alberto Naibo - forthcoming - Studia Logica:1-36.
    We study how to postpone the application of the reductio ad absurdum rule (RAA) in classical natural deduction. This technique is connected with two normalization strategies for classical logic, due to Prawitz and Seldin, respectively. We introduce a variant of Seldin’s strategy for the postponement of RAA, which induces a negative translation from classical to intuitionistic and minimal logic. Through this translation, Glivenko’s theorem from classical to intuitionistic and minimal logic is proven.
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  6.  67
    Proof Theory of Epistemic Logic of Programs.Paolo Maffezioli & Alberto Naibo - 2014 - Logic and Logical Philosophy 23 (3):301--328.
    A combination of epistemic logic and dynamic logic of programs is presented. Although rich enough to formalize some simple game-theoretic scenarios, its axiomatization is problematic as it leads to the paradoxical conclusion that agents are omniscient. A cut-free labelled Gentzen-style proof system is then introduced where knowledge and action, as well as their combinations, are formulated as rules of inference, rather than axioms. This provides a logical framework for reasoning about games in a modular and systematic way, and to give (...)
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  7. The Problem of Harmony in Classical Logic.Giulio Guerrieri & Alberto Naibo - forthcoming - In Martin Blicha & Igor Sedlár (eds.), The Logica Yearbook 2019.
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  8.  16
    An Intuitionistic Logic for Preference Relations.Paolo Maffezioli & Alberto Naibo - 2019 - Logic Journal of the IGPL 27 (4):434-450.
    We investigate in intuitionistic first-order logic various principles of preference relations alternative to the standard ones based on the transitivity and completeness of weak preference. In particular, we suggest two ways in which completeness can be formulated while remaining faithful to the spirit of constructive reasoning, and we prove that the cotransitivity of the strict preference relation is a valid intuitionistic alternative to the transitivity of weak preference. Along the way, we also show that the acyclicity axiom is not finitely (...)
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