11 found
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  1. A logic for factive ignorance.Ekaterina Kubyshkina & Mattia Petrolo - 2019 - Synthese 198 (6):5917-5928.
    In the current debate there are two epistemological approaches to the definition of ignorance: the Standard View and the New View. The former defines ignorance simply as not knowing, while the latter defines it as the absence of true belief. One of the main differences between these two positions lies in rejecting (Standard View) or in accepting (New View) the factivity of ignorance, i.e., if an agent is ignorant of φ, then φ is true. In the present article, we first (...)
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  2.  41
    Keep trusting! A plea for the notion of Trustworthy AI.Giacomo Zanotti, Mattia Petrolo, Daniele Chiffi & Viola Schiaffonati - forthcoming - AI and Society:1-12.
    A lot of attention has recently been devoted to the notion of Trustworthy AI (TAI). However, the very applicability of the notions of trust and trustworthiness to AI systems has been called into question. A purely epistemic account of trust can hardly ground the distinction between trustworthy and merely reliable AI, while it has been argued that insisting on the importance of the trustee’s motivations and goodwill makes the notion of TAI a categorical error. After providing an overview of the (...)
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  3.  26
    Logics of Ignorance and Being Wrong.David Gilbert, Ekaterina Kubyshkina, Mattia Petrolo & Giorgio Venturi - 2022 - Logic Journal of the IGPL 30 (5):870-885.
    This article investigates the connections between the logics of being wrong, introduced in Steinsvold (2011, Notre Dame J. Form. Log., 52, 245–253), and factive ignorance, presented in Kubyshkina and Petrolo (2021, Synthese, 198, 5917–5928). The first part of the paper provides a sound and complete axiomatization of the logic of factive ignorance that corrects errors in Kubyshkina and Petrolo (2021, Synthese, 198, 5917–5928) and resolves questions about the expressivity of the language. In the second half, it is shown that the (...)
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  4.  43
    The Naturality of Natural Deduction.Luca Tranchini, Paolo Pistone & Mattia Petrolo - 2019 - Studia Logica 107 (1):195-231.
    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 only of (...)
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  5. Are Uniqueness and Deducibility of Identicals the Same?Alberto Naibo & Mattia Petrolo - 2014 - 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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  6.  55
    On Paradoxes in Normal Form.Mattia Petrolo & Paolo Pistone - 2019 - Topoi 38 (3):605-617.
    A proof-theoretic test for paradoxicality was famously proposed by Tennant: a paradox must yield a closed derivation of absurdity with no normal form. Drawing on the remark that all derivations of a given proposition can be transformed into derivations in normal form of a logically equivalent proposition, we investigate the possibility of paradoxes in normal form. We compare paradoxes à la Tennant and paradoxes in normal form from the viewpoint of the computational interpretation of proofs and from the viewpoint of (...)
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  7.  25
    The Naturality of Natural Deduction (II): On Atomic Polymorphism and Generalized Propositional Connectives.Paolo Pistone, Luca Tranchini & Mattia Petrolo - 2021 - Studia Logica 110 (2):545-592.
    In a previous paper we investigated the extraction of proof-theoretic properties of natural deduction derivations from their impredicative translation into System F. Our key idea was to introduce an extended equational theory for System F codifying at a syntactic level some properties found in parametric models of polymorphic type theory. A different approach to extract proof-theoretic properties of natural deduction derivations was proposed in a recent series of papers on the basis of an embedding of intuitionistic propositional logic into a (...)
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  8. 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. Cham, Switzerland: 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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  9.  16
    Revising the Elenchus via Belief Revision.Ekaterina Kubyshkina & Mattia Petrolo - 2023 - Logica Universalis 17 (2):231-258.
    Vlastos’ famous characterization of the Socratic elenchus focuses on two main aspects of this method: its epistemic roots and its dialogical nature. Our aim is to lay the groundwork to formally capture this characterization. To do so, first, we outline an epistemic framework in which the elenchus can be inscribed. More precisely, we focus our analysis on the passage from unconscious ignorance to conscious (or Socratic) ignorance and provide new insights about the epistemic outcome of an elenctic argument. Secondly, from (...)
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  10.  26
    What ignorance could not be.Ekaterina Kubyshkina & Mattia Petrolo - 2020 - Principia: An International Journal of Epistemology 24 (2).
    In the current debate there are two epistemological approaches to the definition of ignorance. The Standard View defines ignorance simply as not knowing, while the New View defines it as the absence of true belief. We argue that both views provide necessary, but not sufficient conditions for ignorance, and thus do not constitute satisfactory definitions for such a notion.
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  11. Paradoxes between Truth and Proof.Mattia Petrolo & Giorgio Venturi (eds.) - forthcoming - Springer.
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