10 found
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  1.  23
    Modal‐Type Orthomodular Logic.Graciela Domenech, Hector Freytes & Christian de Ronde - 2009 - Mathematical Logic Quarterly 55 (3):307-319.
    In this paper we enrich the orthomodular structure by adding a modal operator, following a physical motivation. A logical system is developed, obtaining algebraic completeness and completeness with respect to a Kripkestyle semantic founded on Baer*-semigroups as in [22].
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  2.  17
    Pattern Recognition in Non-Kolmogorovian Structures.Federico Holik, Giuseppe Sergioli, Hector Freytes & Angelo Plastino - 2018 - Foundations of Science 23 (1):119-132.
    We present a generalization of the problem of pattern recognition to arbitrary probabilistic models. This version deals with the problem of recognizing an individual pattern among a family of different species or classes of objects which obey probabilistic laws which do not comply with Kolmogorov’s axioms. We show that such a scenario accommodates many important examples, and in particular, we provide a rigorous definition of the classical and the quantum pattern recognition problems, respectively. Our framework allows for the introduction of (...)
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  3.  30
    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.
  4. 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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  5.  86
    Quantum Computational Structures: Categorical Equivalence for Square Root qMV -Algebras.Hector Freytes - 2010 - Studia Logica 95 (1-2):63 - 80.
    In this paper we investigate a categorical equivalence between square root qMV-algehras (a variety of algebras arising from quantum computation) and a category of preordered semigroups.
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  6.  28
    Pavelka-Style Completeness in Expansions of Łukasiewicz Logic.Hector Freytes - 2008 - Archive for Mathematical Logic 47 (1):15-23.
    An algebraic setting for the validity of Pavelka style completeness for some natural expansions of Łukasiewicz logic by new connectives and rational constants is given. This algebraic approach is based on the fact that the standard MV-algebra on the real segment [0, 1] is an injective MV-algebra. In particular the logics associated with MV-algebras with product and with divisible MV-algebras are considered.
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  7.  12
    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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  8.  14
    Physical Properties as Modal Operators in the Topos Approach to Quantum Mechanics.Hector Freytes, Graciela Domenech & Christian de Ronde - 2014 - Foundations of Physics 44 (12):1357-1368.
    In the framework of the topos approach to quantum mechanics we give a representation of physical properties in terms of modal operators on Heyting algebras. It allows us to introduce a classical type study of the mentioned properties.
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  9.  14
    Quantum Computational Logic with Mixed States.Hector Freytes & Graciela Domenech - 2013 - Mathematical Logic Quarterly 59 (1-2):27-50.
    In this paper we solve the problem how to axiomatize a system of quantum computational gates known as the Poincaré irreversible quantum computational system. A Hilbert-style calculus is introduced obtaining a strong completeness theorem.
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  10. Probing the Meaning and Structure of Quantum Mechanics: Semantics, Dynamics and Identity.Diederik Aerts, Christian de Ronde, Hector Freytes & Roberto Giuntini (eds.) - 2016 - World Scientific.
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