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Antonio Ledda
Universita di Cagliari
  1.  71
    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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  2.  7
    Algebraic Analysis of Demodalised Analytic Implication.Antonio Ledda, Francesco Paoli & Michele Pra Baldi - forthcoming - Journal of Philosophical Logic:1-23.
    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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  3.  9
    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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  4.  70
    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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  5. 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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  6.  9
    Representing Quantum Structures as Near Semirings.Stefano Bonzio, Ivan Chajda & Antonio Ledda - 2016 - Logic Journal of the IGPL 24 (5).
  7.  27
    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.
  8. 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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  9.  7
    Introduction: Logical Pluralism and Translation.Francesca Ervas, Antonio Ledda, Francesco Paoli & Giuseppe Sergioli - forthcoming - Topoi:1-2.
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  10.  3
    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.
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  11.  34
    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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  12.  5
    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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  13.  12
    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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  14.  7
    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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