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  1.  6
    Paraconsistent Belief Revision: An Algebraic Investigation.Massimiliano Carrara, Davide Fazio & Michele Pra Baldi - forthcoming - Erkenntnis:1-29.
    This paper offers a logico-algebraic investigation of AGM belief revision based on the logic of paradox ). First, we define a concrete belief revision operator for \, proving that it satisfies a generalised version of the traditional AGM postulates. Moreover, we investigate to what extent the Levi and Harper identities, in their classical formulation, can be applied to a paraconsistent account of revision. We show that a generalised Levi-type identity still yields paraconsistent-based revisions that are fully compatible with the AGM (...)
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  2.  4
    A Substructural Gentzen Calculus for Orthomodular Quantum Logic.Davide Fazio, Antonio Ledda, Francesco Paoli & Gavin St John - forthcoming - Review of Symbolic Logic:1-22.
    We introduce a sequent system which is Gentzen algebraisable with orthomodular lattices as equivalent algebraic semantics, and therefore can be viewed as a calculus for orthomodular quantum logic. Its sequents are pairs of non-associative structures, formed via a structural connective whose algebraic interpretation is the Sasaki product on the left-hand side and its De Morgan dual on the right-hand side. It is a substructural calculus, because some of the standard structural sequent rules are restricted—by lifting all such restrictions, one recovers (...)
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  3.  15
    Algebraic Perspectives on Substructural Logics.Davide Fazio, Antonio Ledda & Francesco Paoli (eds.) - 2020 - Springer International Publishing.
    This volume presents the state of the art in the algebraic investigation into substructural logics. It features papers from the workshop AsubL (Algebra & Substructural Logics - Take 6). Held at the University of Cagliari, Italy, this event is part of the framework of the Horizon 2020 Project SYSMICS: SYntax meets Semantics: Methods, Interactions, and Connections in Substructural logics. -/- Substructural logics are usually formulated as Gentzen systems that lack one or more structural rules. They have been intensively studied over (...)
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  4.  15
    On the Structure Theory of Łukasiewicz Near Semirings.Ivan Chajda, Davide Fazio & Antonio Ledda - 2018 - Logic Journal of the IGPL 26 (1):14-28.
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    Algebraic Properties of Paraorthomodular Posets.Ivan Chajda, Davide Fazio, Helmut Länger, Antonio Ledda & Jan Paseka - forthcoming - Logic Journal of the IGPL.
    Paraorthomodular posets are bounded partially ordered sets with an antitone involution induced by quantum structures arising from the logico-algebraic approach to quantum mechanics. The aim of the present work is starting a systematic inquiry into paraorthomodular posets theory both from algebraic and order-theoretic perspectives. On the one hand, we show that paraorthomodular posets are amenable of an algebraic treatment by means of a smooth representation in terms of bounded directoids with antitone involution. On the other, we investigate their order-theoretical features (...)
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