18 found
Order:
  1.  87
    Interpreting the Modal Kochen–Specker theorem: Possibility and many worlds in quantum mechanics.Christian de Ronde, Hector Freytes & Graciela Domenech - 2014 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 45:11-18.
    In this paper we attempt to physically interpret the Modal Kochen–Specker theorem. In order to do so, we analyze the features of the possible properties of quantum systems arising from the elements in an orthomodular lattice and distinguish the use of “possibility” in the classical and quantum formalisms. Taking into account the modal and many worlds non-collapse interpretation of the projection postulate, we discuss how the MKS theorem rules the constraints to actualization, and thus, the relation between actual and possible (...)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   12 citations  
  2.  22
    Quantum mechanics and the interpretation of the orthomodular square of opposition.Christian de Ronde, Hector Freytes & Graciela Domenech - unknown
    In this paper we analyze and discuss the historical and philosophical development of the notion of logical possibility focusing on its specific meaning in classical and quantum mechanics. Taking into account the logical structure of quantum theory we continue our discussion regarding the Aristotelian Square of Opposition in orthomodular structures enriched with a monadic quantifier. Finally, we provide an interpretation of the Orthomodular Square of Opposition exposing the fact that classical possibility and quantum possibility behave formally in radically different manners.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   8 citations  
  3.  43
    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].
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  4.  25
    The square of opposition in orthomodular logic.Hector Freytes, Christian de Ronde & Graciela Domenech - unknown
    In Aristotelian logic, categorical propositions are divided in Universal Affirmative, Universal Negative, Particular Affirmative and Particular Negative. Possible relations between two of the mentioned type of propositions are encoded in the square of opposition. The square expresses the essential properties of monadic first order quantification which, in an algebraic approach, may be represented taking into account monadic Boolean algebras. More precisely, quantifiers are considered as modal operators acting on a Boolean algebra and the square of opposition is represented by relations (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  5. 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; (...)
     
    Export citation  
     
    Bookmark   3 citations  
  6.  55
    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 (the closed disc with center \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(\frac{1}{2},\frac{1}{2})$\end{document} and radius \documentclass[12pt]{minimal} (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  7.  47
    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 (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  8.  14
    Heyting $$\kappa $$-Frames.Hector Freytes & Giuseppe Sergioli - forthcoming - Studia Logica:1-44.
    In the framework of algebras with infinitary operations, the equational theory of $$\bigvee _{\kappa }$$ ⋁ κ -complete Heyting algebras or Heyting $$\kappa $$ κ -frames is studied. A Hilbert style calculus algebraizable in this class is formulated. Based on the infinitary structure of Heyting $$\kappa $$ κ -frames, an equational type completeness theorem related to the $$\langle \bigvee, \wedge, \rightarrow, 0 \rangle $$ ⟨ ⋁, ∧, →, 0 ⟩ -structure of frames is also obtained.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  9.  3
    Heyting $$\kappa $$ -Frames.Hector Freytes & Giuseppe Sergioli - 2024 - Studia Logica 112 (4):761-804.
    In the framework of algebras with infinitary operations, the equational theory of \(\bigvee _{\kappa }\) -complete Heyting algebras or Heyting \(\kappa \) -frames is studied. A Hilbert style calculus algebraizable in this class is formulated. Based on the infinitary structure of Heyting \(\kappa \) -frames, an equational type completeness theorem related to the \(\langle \bigvee, \wedge, \rightarrow, 0 \rangle \) -structure of frames is also obtained.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  10.  43
    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.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  11.  24
    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.
    Direct download  
     
    Export citation  
     
    Bookmark  
  12.  28
    The contextual character of modal interpretations of quantum mechanics.Graciela Domenech, Hector Freytes & Christian de Ronde - unknown
    In this article we discuss the contextual character of quantum mechanics in the framework of modal interpretations. We investigate its historical origin and relate contemporary modal interpretations to those proposed by M. Born and W. Heisenberg. We present then a general characterization of what we consider to be a modal interpretation. Following previous papers in which we have introduced modalities in the Kochen-Specker theorem, we investigate the consequences of these theorems in relation to the modal interpretations of quantum mechanics.
    Direct download  
     
    Export citation  
     
    Bookmark  
  13.  73
    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.
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark  
  14.  52
    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.
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark  
  15. 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.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  16. 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.
    No categories
     
    Export citation  
     
    Bookmark  
  17. Fredkin and Toffoli quantum gates: fuzzy representations and comparison.Ranjith Venkatrama, Giuseppe Sergioli, Hector Freytes & Roberto Leporini - 2019 - In Diederik Aerts, Dalla Chiara, Maria Luisa, Christian de Ronde & Decio Krause (eds.), Probing the meaning of quantum mechanics: information, contextuality, relationalism and entanglement: Proceedings of the II International Workshop on Quantum Mechanics and Quantum Information: Physical, Philosophical and Logical Approaches, CLEA, Brussels. New Jersey: World Scientific.
     
    Export citation  
     
    Bookmark  
  18.  14
    Probing the meaning of quantum mechanics: superpositions, dynamics, semantics and identity: Quantum Mechanics and Quantum Information: Physical, Philosophical and Logical Approaches, Cagliari, Italy, 23-25 July 2014.Diederik Aerts, Christian de Ronde, Hector Freytes & Roberto Giuntini (eds.) - 2016 - New Jersey: World Scientific.
    This book provides an interdisciplinary approach to one of the most fascinating and important open questions in science: What is quantum mechanics really talking about? In the last decades quantum mechanics has given rise to a new quantum technological era, a revolution taking place today especially within the field of quantum information processing; which goes from quantum teleportation and cryptography to quantum computation. Quantum theory is probably our best confirmed physical theory. However, in spite of its great empirical effectiveness it (...)
    No categories
    Direct download  
     
    Export citation  
     
    Bookmark