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Antonio Ledda [17]A. Ledda [8]
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  1.  18
    Algebraic Analysis of Demodalised Analytic Implication.Antonio Ledda, Francesco Paoli & Michele Pra Baldi - 2019 - Journal of Philosophical Logic 48 (6):957-979.
    The logic DAI of demodalised analytic implication has been introduced by J.M. Dunn as a variation on a time-honoured logical system by C.I. Lewis’ student W.T. Parry. The main tenet underlying this logic is that no implication can be valid unless its consequent is “analytically contained” in its antecedent. DAI has been investigated both proof-theoretically and model-theoretically, but no study so far has focussed on DAI from the viewpoint of abstract algebraic logic. We provide several different algebraic semantics for DAI, (...)
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  2.  33
    Creative Argumentation: When and Why People Commit the Metaphoric Fallacy.Francesca Ervas, Antonio Ledda, Amitash Ojha, Giuseppe Antonio Pierro & Bipin Indurkhya - 2018 - Frontiers in Psychology 9.
  3.  74
    MV-Algebras and Quantum Computation.Antonio Ledda, Martinvaldo Konig, Francesco Paoli & Roberto Giuntini - 2006 - Studia Logica 82 (2):245-270.
    We introduce a generalization of MV algebras motivated by the investigations into the structure of quantum logical gates. After laying down the foundations of the structure theory for such quasi-MV algebras, we show that every quasi-MV algebra is embeddable into the direct product of an MV algebra and a “flat” quasi-MV algebra, and prove a completeness result w.r.t. a standard quasi-MV algebra over the complex numbers.
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  4.  18
    Stone-Type Representations and Dualities for Varieties of Bisemilattices.Antonio Ledda - 2018 - Studia Logica 106 (2):417-448.
    In this article we will focus our attention on the variety of distributive bisemilattices and some linguistic expansions thereof: bounded, De Morgan, and involutive bisemilattices. After extending Balbes’ representation theorem to bounded, De Morgan, and involutive bisemilattices, we make use of Hartonas–Dunn duality and introduce the categories of 2spaces and 2spaces\. The categories of 2spaces and 2spaces\ will play with respect to the categories of distributive bisemilattices and De Morgan bisemilattices, respectively, a role analogous to the category of Stone spaces (...)
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  5.  22
    A New View of Effects in a Hilbert Space.Roberto Giuntini, Antonio Ledda & Francesco Paoli - 2016 - Studia Logica 104 (6):1145-1177.
    We investigate certain Brouwer-Zadeh lattices that serve as abstract counterparts of lattices of effects in Hilbert spaces under the spectral ordering. These algebras, called PBZ*-lattices, can also be seen as generalisations of orthomodular lattices and are remarkable for the collapse of three notions of “sharpness” that are distinct in general Brouwer-Zadeh lattices. We investigate the structure theory of PBZ*-lattices and their reducts; in particular, we prove some embedding results for PBZ*-lattices and provide an initial description of the lattice of PBZ*-varieties.
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  6.  3
    On Finch’s Conditions for the Completion of Orthomodular Posets.D. Fazio, A. Ledda & F. Paoli - forthcoming - Foundations of Science:1-22.
    In this paper, we aim at highlighting the significance of the A- and B-properties introduced by Finch. These conditions turn out to capture interesting structural features of lattices of closed subspaces of complete inner vector spaces. Moreover, we generalise them to the context of effect algebras, establishing a novel connection between quantum structures arising from the logico-algebraic approach to quantum mechanics.
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  7.  21
    Representing Quantum Structures as Near Semirings.Stefano Bonzio, Ivan Chajda & Antonio Ledda - 2016 - Logic Journal of the IGPL 24 (5).
  8.  72
    Expanding Quasi-MV Algebras by a Quantum Operator.Roberto Giuntini, Antonio Ledda & Francesco Paoli - 2007 - Studia Logica 87 (1):99-128.
    We investigate an expansion of quasi-MV algebras ([10]) by a genuine quantum unary operator. The variety of such quasi-MV algebras has a subquasivariety whose members—called cartesian—can be obtained in an appropriate way out of MV algebras. After showing that cartesian . quasi-MV algebras generate ,we prove a standard completeness theorem for w.r.t. an algebra over the complex numbers.
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  9. On Some Properties of Quasi-MV Algebras and $\sqrt{^{\prime }}$ Quasi-MV Algebras.Francesco Paoli, Antonio Ledda, Roberto Giuntini & Hector Freytes - 2009 - Reports on Mathematical Logic:31-63.
    We investigate some properties of two varieties of algebras arising from quantum computation - quasi-MV algebras and $\sqrt{^{\prime }}$ quasi-MV algebras - first introduced in \cite{Ledda et al. 2006}, \cite{Giuntini et al. 200+} and tightly connected with fuzzy logic. We establish the finite model property and the congruence extension property for both varieties; we characterize the quasi-MV reducts and subreducts of $\sqrt{^{\prime }}$ quasi-MV algebras; we give a representation of semisimple $\sqrt{^{\prime }}$ quasi-MV algebras in terms of algebras of functions; (...)
     
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  10.  37
    The Algebraic Structure of an Approximately Universal System of Quantum Computational Gates.Maria Luisa Dalla Chiara, Roberto Giuntini, Hector Freytes, Antonio Ledda & Giuseppe Sergioli - 2009 - Foundations of Physics 39 (6):559-572.
    Shi and Aharonov have shown that the Toffoli gate and the Hadamard gate give rise to an approximately universal set of quantum computational gates. We study the basic algebraic properties of this system by introducing the notion of Shi-Aharonov quantum computational structure. We show that the quotient of this structure is isomorphic to a structure based on a particular set of complex numbers $\end{document} and radius \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\frac{1}{2}$\end{document} ).
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  11.  2
    Residuated Structures and Orthomodular Lattices.D. Fazio, A. Ledda & F. Paoli - 2021 - Studia Logica 109 (6):1201-1239.
    The variety of residuated lattices includes a vast proportion of the classes of algebras that are relevant for algebraic logic, e.g., \-groups, Heyting algebras, MV-algebras, or De Morgan monoids. Among the outliers, one counts orthomodular lattices and other varieties of quantum algebras. We suggest a common framework—pointed left-residuated \-groupoids—where residuated structures and quantum structures can all be accommodated. We investigate the lattice of subvarieties of pointed left-residuated \-groupoids, their ideals, and develop a theory of left nuclei. Finally, we extend some (...)
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  12. Entanglement as a Semantic Resource.Maria Luisa Dalla Chiara, Roberto Giuntini, Antonio Ledda, Roberto Leporini & Giuseppe Sergioli - 2010 - Foundations of Physics 40 (9-10):1494-1518.
    The characteristic holistic features of the quantum theoretic formalism and the intriguing notion of entanglement can be applied to a field that is far from microphysics: logical semantics. Quantum computational logics are new forms of quantum logic that have been suggested by the theory of quantum logical gates in quantum computation. In the standard semantics of these logics, sentences denote quantum information quantities: systems of qubits (quregisters) or, more generally, mixtures of quregisters (qumixes), while logical connectives are interpreted as special (...)
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  13.  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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  14.  33
    The Lattice of Subvarieties of $${\sqrt{\prime}}$$ Quasi-MV Algebras.T. Kowalski, F. Paoli, R. Giuntini & A. Ledda - 2010 - Studia Logica 95 (1-2):37-61.
    In the present paper we continue the investigation of the lattice of subvarieties of the variety of ${\sqrt{\prime}}$ quasi-MV algebras, already started in [6]. Beside some general results on the structure of such a lattice, the main contribution of this work is the solution of a long-standing open problem concerning these algebras: namely, we show that the variety generated by the standard disk algebra D r is not finitely based, and we provide an infinite equational basis for the same variety.
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  15.  40
    The Toffoli-Hadamard Gate System: An Algebraic Approach.Maria Luisa Dalla Chiara, Antonio Ledda, Giuseppe Sergioli & Roberto Giuntini - 2013 - Journal of Philosophical Logic 42 (3):467-481.
    Shi and Aharonov have shown that the Toffoli gate and the Hadamard gate give rise to an approximately universal set of quantum computational gates. The basic algebraic properties of this system have been studied in Dalla Chiara et al. (Foundations of Physics 39(6):559–572, 2009), where we have introduced the notion of Shi-Aharonov quantum computational structure. In this paper we propose an algebraic abstraction from the Hilbert-space quantum computational structures, by introducing the notion of Toffoli-Hadamard algebra. From an intuitive point of (...)
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  16.  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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  17. New Directions in Logic and the Philosophy of Science.L. Felline, A. Ledda, F. Paoli & E. Rossanese (eds.) - 2016 - College Publications.
  18.  20
    Introduction: Logical Pluralism and Translation.Francesca Ervas, Antonio Ledda, Francesco Paoli & Giuseppe Sergioli - 2019 - Topoi 38 (2):263-264.
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  19.  15
    The Lattice of Subvarieties of √′ Quasi-MV Algebras.T. Kowalski, F. Paoli, R. Giuntini & A. Ledda - 2010 - Studia Logica 95 (1-2):37 - 61.
    In the present paper we continue the investigation of the lattice of subvarieties of the variety of √′ P quasi-MV algebras, already started in [6]. Beside some general results on the structure of such a lattice, the main contribution of this work is the solution of a long-standing open problem concerning these algebras: namely, we show that the variety generated by the standard disk algebra D r is not finitely based, and we provide an infinite equational basis for the same (...)
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  20.  39
    On Certain Quasivarieties of Quasi-MV Algebras.A. Ledda, T. Kowalski & F. Paoli - 2011 - Studia Logica 98 (1-2):149-174.
    Quasi-MV algebras are generalisations of MV algebras arising in quantum computational logic. Although a reasonably complete description of the lattice of subvarieties of quasi-MV algebras has already been provided, the problem of extending this description to the setting of quasivarieties has so far remained open. Given its apparent logical repercussions, we tackle the issue in the present paper. We especially focus on quasivarieties whose generators either are subalgebras of the standard square quasi-MV algebra S , or can be obtained therefrom (...)
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  21.  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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  22.  6
    Classical Logic with N Truth Values as a Symmetric Many-Valued Logic.A. Salibra, A. Bucciarelli, A. Ledda & F. Paoli - forthcoming - Foundations of Science:1-28.
    We introduce Boolean-like algebras of dimension n having n constants $${{{\mathsf {e}}}}_1,\ldots,{{{\mathsf {e}}}}_n$$ e 1, …, e n, and an $$$$ -ary operation q that induces a decomposition of the algebra into n factors through the so-called n-central elements. Varieties of $$n{\mathrm {BA}}$$ n BA s share many remarkable properties with the variety of Boolean algebras and with primal varieties. The $$n{\mathrm {BA}}$$ n BA s provide the algebraic framework for generalising the classical propositional calculus to the case of n–perfectly (...)
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  23.  14
    Completion and Amalgamation of Bounded Distributive Quasi Lattices.Majid Alizadeh, Antonio Ledda & Hector Freytes - 2011 - Logic Journal of the IGPL 19 (1):110-120.
    In this note we present a completion for the variety of bounded distributive quasi lattices, and, inspired by a well-known idea of L.L. Maksimova [14], we apply this result in proving the amalgamation property for such a class of algebras.
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  24.  6
    Quasi-Subtractive Varieties: Open Filters, Congruences and the Commutator.T. Kowalski, A. Ledda & F. Paoli - 2014 - Logic Journal of the IGPL 22 (6):844-871.
  25.  2
    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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