This category needs an editor. We encourage you to help if you are qualified.
Volunteer, or read more about what this involves.
Related

Contents
572 found
Order:
1 — 50 / 572
  1. Chess composition as an art.Miro Brada - manuscript
    The article presents the chess composition as a logical art, with concrete examples. It began with Arabic mansuba, and later evolved to new-strategy designed by Italian Alberto Mari. The redefinition of mate (e.g. mate with a free field) or a theme to quasi-pseudo theme, opens the new space for combinations, and enables to connect it with other fields like computer science. The article was exhibited in Holland Park, W8 6LU, The Ice House between 18. Oct - 3. Nov. 2013.
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  2. On Classical and Quantum Logical Entropy.David Ellerman - manuscript
    The notion of a partition on a set is mathematically dual to the notion of a subset of a set, so there is a logic of partitions dual to Boole's logic of subsets (Boolean logic is usually mis-specified as "propositional" logic). The notion of an element of a subset has as its dual the notion of a distinction of a partition (a pair of elements in different blocks). Boole developed finite logical probability as the normalized counting measure on elements of (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  3. On the duality between existence and information.David Ellerman - manuscript
    Recent developments in pure mathematics and in mathematical logic have uncovered a fundamental duality between "existence" and "information." In logic, the duality is between the Boolean logic of subsets and the logic of quotient sets, equivalence relations, or partitions. The analogue to an element of a subset is the notion of a distinction of a partition, and that leads to a whole stream of dualities or analogies--including the development of new logical foundations for information theory parallel to Boole's development of (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  4. Partitions and Objective Indefiniteness.David Ellerman - manuscript
    Classical physics and quantum physics suggest two meta-physical types of reality: the classical notion of a objectively definite reality with properties "all the way down," and the quantum notion of an objectively indefinite type of reality. The problem of interpreting quantum mechanics (QM) is essentially the problem of making sense out of an objectively indefinite reality. These two types of reality can be respectively associated with the two mathematical concepts of subsets and quotient sets (or partitions) which are category-theoretically dual (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  5. Heisenberg quantum mechanics, numeral set-theory and.Han Geurdes - manuscript
    In the paper we will employ set theory to study the formal aspects of quantum mechanics without explicitly making use of space-time. It is demonstrated that von Neuman and Zermelo numeral sets, previously efectively used in the explanation of Hardy’s paradox, follow a Heisenberg quantum form. Here monadic union plays the role of time derivative. The logical counterpart of monadic union plays the part of the Hamiltonian in the commutator. The use of numerals and monadic union in the classical probability (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  6. Quantum behavior of the systems with a single degree of freedom and the derivation of quantum theory.Mehran Shaghaghi - manuscript
    The number of independent messages a physical system can carry is limited by the number of its adjustable properties. In particular, systems that have only one adjustable property cannot carry more than a single message at a time. We demonstrate this is the case for the single photons in the double-slit experiment, and the root of the fundamental limit on measuring the complementary aspect of the photons. Next, we analyze the other ‘quantal’ behavior of the systems with a single adjustable (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  7. Standard Quantum Theory Derived from First Physical Principles.Mehran Shaghaghi - manuscript
    The mathematical formalism of quantum theory has been known for almost a century, but its physical foundation has remained elusive. In recent decades, many physicists have noted connections between quantum theory and information theory. In this study, we present a physical account of the derivation of quantum theory's mathematical formalism based on information considerations in physical systems. We postulate that quantum systems are physical systems with only one independent adjustable variable. Using this physical postulate along with the conservation of the (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  8. Rules and Meaning in Quantum Mechanics.Iulian D. Toader - manuscript
    This book concerns the metasemantics of quantum mechanics (QM). Roughly, it pursues an investigation at an intersection of the philosophy of physics and the philosophy of semantics, and it offers a critical analysis of rival explanations of the semantic facts of standard QM. Two problems for such explanations are discussed: categoricity and permanence of rules. New results include 1) a reconstruction of Einstein's incompleteness argument, which concludes that a local, separable, and categorical QM cannot exist, 2) a reinterpretation of Bohr's (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  9. The Quantum Logic of Direct-Sum Decompositions: The Dual to the Quantum Logic of Subspaces.David Ellerman - 2017
    Since the pioneering work of Birkhoff and von Neumann, quantum logic has been interpreted as the logic of (closed) subspaces of a Hilbert space. There is a progression from the usual Boolean logic of subsets to the "quantum logic" of subspaces of a general vector space--which is then specialized to the closed subspaces of a Hilbert space. But there is a "dual" progression. The notion of a partition (or quotient set or equivalence relation) is dual (in a category-theoretic sense) to (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  10. What is Logical Monism?Justin Clarke-Doane - forthcoming - In Christopher Peacocke & Paul Boghossian (eds.), Normative Realism. Oxford University Press.
    Logical monism is the view that there is ‘One True Logic’. This is the default position, against which pluralists react. If there were not ‘One True Logic’, it is hard to see how there could be one true theory of anything. A theory is closed under a logic! But what is logical monism? In this article, I consider semantic, logical, modal, scientific, and metaphysical proposals. I argue that, on no ‘factualist’ analysis (according to which ‘there is One True Logic’ expresses (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  11. Compatibility, compossibility, and epistemic modality.Wesley Holliday & Matthew Mandelkern - forthcoming - Proceedings of the 23rd Amsterdam Colloquium.
    We give a theory of epistemic modals in the framework of possibility semantics and axiomatize the corresponding logic, arguing that it aptly characterizes the ways in which reasoning with epistemic modals does, and does not, diverge from classical modal logic.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  12. Generalized fuzzy quantum logics.J. Pykacz - forthcoming - Foundations of Physics.
    Remove from this list  
     
    Export citation  
     
    Bookmark  
  13. Modal-type orthomodular logic.Trixie Wagner & Andreas Schouml - forthcoming - Mathematical Logic Quarterly.
    Remove from this list  
     
    Export citation  
     
    Bookmark   1 citation  
  14. On J. Czelakowski’s Contributions to Quantum Logic and the Foundation of Quantum Mechanics.Davide Fazio - 2024 - In Jacek Malinowski & Rafał Palczewski (eds.), Janusz Czelakowski on Logical Consequence. Springer Verlag. pp. 233-264.
    This paper provides an overview of Janusz Czelakowski’s contributions to the theory of partial Boolean (σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma $$\end{document}-)algebras, and, more in general, to the foundation of Quantum Mechanics. Particular attention is paid to the logic of partial Boolean σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma $$\end{document}-algebras, to characterizations of PBAs embeddable into Boolean (σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma $$\end{document}-)algebras, and their representation as self-adjoint idempotent (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  15. An Alleged Tension between non-Classical Logics and Applied Classical Mathematics.Sebastian Horvat & Iulian D. Toader - 2024 - The Philosophical Quarterly 1:1-19.
    Timothy Williamson has maintained that the applicability of classical mathematics in science raises a problem for the endorsement, in non-mathematical domains, of a wide range of non-classical logics. We show that this is false.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  16. A Substructural Gentzen Calculus for Orthomodular Quantum Logic.Davide Fazio, Antonio Ledda, Francesco Paoli & Gavin St John - 2023 - Review of Symbolic Logic 16 (4):1177-1198.
    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 (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  17. La interpretación modal de la mecánica cuántica: de la lógica cuántica al problema de la medida.Jose Alejandro Fernández Cuesta - 2023 - Revista de la Sociedad de Lógica, Metodología y Filosofía de la Ciencia En España:14-36.
    El presente trabajo pretende explicitar que los operadores modales, como construcciones lógicas, insertos en las interpretaciones modales (MI) de la mecánica cuántica son usados de manera informal sin una semántica modal adecuada. Primero se estudiarán en detalle los motivos por los que ninguna lógica cuántica puede ofrecer una base apropiada para formalizar estos operadores en contextos mecánico-cuánticos. A continuación, se presentará el enfoque de las historias cuánticas como una nueva lógica cuántica (NQL) intrínsecamente booleana como posible herramienta para formalizar operadores (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  18. Contrafácticos cuánticos: aproximación lógico-filosófica a las medidas cuánticas sin interacción.Jose Alejandro Fernandez Cuesta & Carmen Sánchez Ovcharov - 2023 - Revista Colombiana de Filosofía de la Ciencia 23 (46):313-337.
    Este artículo presenta una aproximación lógico-filosófica al problema de las medidas sin interacción (ifm, por sus siglas en inglés) presentes en ciertos experimentos físicos mecánico-cuánticos. Se explicitarán tanto las posibles vías para abordar el estudio de las IFM desde una perspectiva formal, como algunos de los principales retos a la hora de llevar a cabo dicha aproximación.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  19. A fundamental non-classical logic.Wesley Holliday - 2023 - Logics 1 (1):36-79.
    We give a proof-theoretic as well as a semantic characterization of a logic in the signature with conjunction, disjunction, negation, and the universal and existential quantifiers that we suggest has a certain fundamental status. We present a Fitch-style natural deduction system for the logic that contains only the introduction and elimination rules for the logical constants. From this starting point, if one adds the rule that Fitch called Reiteration, one obtains a proof system for intuitionistic logic in the given signature; (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  20. Broken Arrows: Hardy–Unruh Chains and Quantum Contextuality.Michael Janas & Michel Janssen - 2023 - Entropy 25 (12):1568.
    Hardy and Unruh constructed a family of non-maximally entangled states of pairs of particles giving rise to correlations that cannot be accounted for with a local hidden-variable theory. Rather than pointing to violations of some Bell inequality, however, they pointed to apparent clashes with the basic rules of logic. Specifically, they constructed these states and the associated measurement settings in such a way that the outcomes satisfy some conditionals but not an additional one entailed by them. Quantum mechanics avoids the (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  21. Quantum Logic for Observation of Physical Quantities.Tomoaki Kawano - 2023 - In Carlos Areces & Diana Costa (eds.), Dynamic Logic. New Trends and Applications: 4th International Workshop, DaLí 2022, Haifa, Israel, July 31–August 1, 2022, Revised Selected Papers. Springer Verlag. pp. 90-105.
    Dynamic quantum logic (DQL) is studied to represent the proposition of dynamism in quantum information theory as traditional quantum logic cannot deal with it. Although DQL includes many important notions for quantum physics and quantum information theory, there are still missing elements. Some concepts of measuring a specific physical quantity cannot be represented in the exiting DQL. In this study, we add a new concept of measurement to DQL, and discuss the property of this new logic.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  22. The Question of Logic.Saul A. Kripke - 2023 - Mind 133 (529):1-36.
    Under the influence of Quine’s famous manifesto, many philosophers have thought that logical theories are scientific theories that can be ‘adopted’ and tested as scientific theories. Here we argue that this idea is untenable. We discuss it with special reference to Putnam’s proposal to ‘adopt’ a particular non-classical logic to solve the foundational problems of quantum mechanics in his famous paper ‘Is Logic Empirical?’ (1968), which we argue was not really coherent.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  23. The Tik-Tok Universe.Ilexa Yardley - 2023 - Https://Medium.Com/the-Circular-Theory/.
  24. Compatibility and accessibility: lattice representations for semantics of non-classical and modal logics.Wesley Holliday - 2022 - In David Fernández Duque, Alessandra Palmigiano & Sophie Pinchinat (eds.), Advances in Modal Logic, Vol. 14. London: College Publications. pp. 507-529.
    In this paper, we study three representations of lattices by means of a set with a binary relation of compatibility in the tradition of Ploščica. The standard representations of complete ortholattices and complete perfect Heyting algebras drop out as special cases of the first representation, while the second covers arbitrary complete lattices, as well as complete lattices equipped with a negation we call a protocomplementation. The third topological representation is a variant of that of Craig, Haviar, and Priestley. We then (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  25. Lógica cuántica, Nmatrices y adecuación, I (3rd edition).Juan Pablo Jorge & Federico Holik - 2022 - Teorema: International Journal of Philosophy 41 (3):65-88.
    In this paper we discuss the notions of adequacy and truth functionality in quantum logic from the point of view of a non-deterministic semantics. We give a characterization of the degree of non-functionality which is compatible with the propositional structure of quantum theory, showing that having truth-functional connectives, together with some assumptions regarding the relation of logical consequence, commits us to the adequacy of the interpretation sets of these connectives. An advantage of our proof is that it is independent of (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  26. The Labyrinth of Quantum Logic.Tim Maudlin - 2022 - In Sanjit Chakraborty & James Ferguson Conant (eds.), Engaging Putnam. De Gruyter. pp. 183-206.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  27. MASS SURVEILLANCE, BEHAVIOURAL CONTROL, AND PSYCHOLOGICAL COERCION THE MORAL ETHICAL RISKS IN COMMERCIAL DEVICES.Yang Immanuel Pachankis - 2022 - In David C. Wyld & Dhinaharan Nagamalai (eds.), Computer Science and Information Technology. Chennai, India: pp. 151-168.
    The research observed, in parallel and comparatively, a surveillance state’s use of communication & cyber networks with satellite applications for power political & realpolitik purposes, in contrast to the outer space security & legit scientific purpose driven cybernetics. The research adopted a psychoanalytic & psychosocial method of observation in the organizational behaviors of the surveillance state, and a theoretical physics, astrochemical, & cosmological feedback method in the contrast group of cybernetics. Military sociology and multilateral movements were adopted in the diagnostic (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  28. On the Strangeness of Quantum Mechanics.Marcello Poletti - 2022 - Foundations of Physics 52 (3):1-7.
    The extravagances of quantum mechanics never fail to enrich daily the debate around natural philosophy. Entanglement, non-locality, collapse, many worlds, many minds, and subjectivism have challenged generations of thinkers. Its approach can perhaps be placed in the stream of quantum logic, in which the “strangeness” of QM is “measured” through the violation of Bell’s inequalities and, from there, attempts an interpretative path that preserves realism yet ends up overturning it, restating the fundamental mechanisms of QM as a logical necessity for (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  29. Natural Deduction for Quantum Logic.K. Tokuo - 2022 - Logica Universalis 16 (3):469-497.
    This paper presents a natural deduction system for orthomodular quantum logic. The system is shown to be provably equivalent to Nishimura’s quantum sequent calculus. Through the Curry–Howard isomorphism, quantum $$\lambda $$ -calculus is also introduced for which strong normalization property is established.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  30. Implicational quantum logic.Kenji Tokuo - 2022 - Axiomathes 32 (2):473-483.
    A non-classical subsystem of orthomodular quantum logic is proposed. This system employs two basic operations: the Sasaki hook as implication and the _and-then_ operation as conjunction. These operations successfully satisfy modus ponens and the deduction theorem. In other words, they form an adjunction in terms of category theory. Two types of semantics are presented for this logic: one algebraic and one physical. The algebraic semantics deals with orthomodular lattices, as in traditional quantum logic. The physical semantics is given as a (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  31. On Abstraction in Mathematics and Indefiniteness in Quantum Mechanics.David Ellerman - 2021 - Journal of Philosophical Logic 50 (4):813-835.
    ion turns equivalence into identity, but there are two ways to do it. Given the equivalence relation of parallelness on lines, the #1 way to turn equivalence into identity by abstraction is to consider equivalence classes of parallel lines. The #2 way is to consider the abstract notion of the direction of parallel lines. This paper developments simple mathematical models of both types of abstraction and shows, for instance, how finite probability theory can be interpreted using #2 abstracts as “superposition (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  32. Two quantum logics of indeterminacy.Samuel C. Fletcher & David E. Taylor - 2021 - Synthese 199 (5-6):13247-13281.
    We implement a recent characterization of metaphysical indeterminacy in the context of orthodox quantum theory, developing the syntax and semantics of two propositional logics equipped with determinacy and indeterminacy operators. These logics, which extend a novel semantics for standard quantum logic that accounts for Hilbert spaces with superselection sectors, preserve different desirable features of quantum logic and logics of indeterminacy. In addition to comparing the relative advantages of the two, we also explain how each logic answers Williamson’s challenge to any (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  33. A Few Notes on Quantum B-algebras.Shengwei Han & Xiaoting Xu - 2021 - Studia Logica 109 (6):1423-1440.
    In order to provide a unified framework for studying non-commutative algebraic logic, Rump and Yang used three axioms to define quantum B-algebras, which can be seen as implicational subreducts of quantales. Based on the work of Rump and Yang, in this paper we shall continue to investigate the properties of three axioms in quantum B-algebras. First, using two axioms we introduce the concept of generalized quantum B-algebras and prove that the opposite of the category GqBAlg of generalized quantum B-algebras is (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  34. Lattice Logic, Bilattice Logic and Paraconsistent Quantum Logic: a Unified Framework Based on Monosequent Systems.Norihiro Kamide - 2021 - Journal of Philosophical Logic 50 (4):781-811.
    Lattice logic, bilattice logic, and paraconsistent quantum logic are investigated based on monosequent systems. Paraconsistent quantum logic is an extension of lattice logic, and bilattice logic is an extension of paraconsistent quantum logic. Monosequent system is a sequent calculus based on the restricted sequent that contains exactly one formula in both the antecedent and succedent. It is known that a completeness theorem with respect to a lattice-valued semantics holds for a monosequent system for lattice logic. A completeness theorem with respect (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  35. Quantum set theory: Transfer Principle and De Morgan's Laws.Masanao Ozawa - 2021 - Annals of Pure and Applied Logic 172 (4):102938.
    In quantum logic, introduced by Birkhoff and von Neumann, De Morgan's Laws play an important role in the projection-valued truth value assignment of observational propositions in quantum mechanics. Takeuti's quantum set theory extends this assignment to all the set-theoretical statements on the universe of quantum sets. However, Takeuti's quantum set theory has a problem in that De Morgan's Laws do not hold between universal and existential bounded quantifiers. Here, we solve this problem by introducing a new truth value assignment for (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  36. Quantum metametaphysics.Alessandro Torza - 2021 - Synthese 199 (3-4):1-25.
    Say that metaphysical indeterminacy occurs just when there is a fact such that neither it nor its negation obtains. The aim of this work is to shed light on the issue of whether orthodox quantum mechanics provides any evidence of metaphysical indeterminacy by discussing the logical, semantic, and broadly methodological presuppositions of the debate. I argue that the dispute amounts to a verbal disagreement between classical and quantum logicians, given Eli Hirsch’s account of substantivity; but that it need not be (...)
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  37. Implications of quantum logic to the notion of transcendence.Jerome P. Manyahi - 2020 - Delhi: Indian Society for Promoting Christian Knowledge. Edited by Francis P. Xavier.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  38. Universal Logic in terms of Quantum Information.Vasil Penchev - 2020 - Metaphilosophy eJournal (Elsevier: SSRN) 12 (9):1-5.
    Any logic is represented as a certain collection of well-orderings admitting or not some algebraic structure such as a generalized lattice. Then universal logic should refer to the class of all subclasses of all well-orderings. One can construct a mapping between Hilbert space and the class of all logics. Thus there exists a correspondence between universal logic and the world if the latter is considered a collection of wave functions, as which the points in Hilbert space can be interpreted. The (...)
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  39. Pan demos Alla ricerca di un nuovo pensiero.Donato Santarcangelo - 2020 - Dialoghi Mediterranei.
  40. Categoricity and Possibility. A Note on Williamson's Modal Monism.Iulian D. Toader - 2020 - In The Logica Yearbook 2019. London: College Publications. pp. 221-231.
    The paper sketches an argument against modal monism, more specifically against the reduction of physical possibility to metaphysical possibility. The argument is based on the non-categoricity of quantum logic.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  41. The Quantum Logic of Direct-Sum Decompositions: The Dual to the Quantum Logic of Subspaces.David Ellerman - 2018 - Logic Journal of the IGPL 26 (1):1-13.
    ince the pioneering work of Birkhoff and von Neumann, quantum logic has been interpreted as the logic of subspaces of a Hilbert space. There is a progression from the usual Boolean logic of subsets to the "quantum logic" of subspaces of a general vector space--which is then specialized to the closed subspaces of a Hilbert space. But there is a "dual" progression. The set notion of a partition is dual to the notion of a subset. Hence the Boolean logic of (...)
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  42. Topos Theoretic Quantum Realism.Benjamin Eva - 2017 - British Journal for the Philosophy of Science 68 (4):1149-1181.
    ABSTRACT Topos quantum theory is standardly portrayed as a kind of ‘neo-realist’ reformulation of quantum mechanics.1 1 In this article, I study the extent to which TQT can really be characterized as a realist formulation of the theory, and examine the question of whether the kind of realism that is provided by TQT satisfies the philosophical motivations that are usually associated with the search for a realist reformulation of quantum theory. Specifically, I show that the notion of the quantum state (...)
    Remove from this list   Direct download (8 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  43. The logic of the future in quantum theory.Anthony Sudbery - 2017 - Synthese 194 (11):4429-4453.
    According to quantum mechanics, statements about the future made by sentient beings like us are, in general, neither true nor false; they must satisfy a many-valued logic. I propose that the truth value of such a statement should be identified with the probability that the event it describes will occur. After reviewing the history of related ideas in logic, I argue that it gives an understanding of probability which is particularly satisfactory for use in quantum mechanics. I construct a lattice (...)
    Remove from this list   Direct download (6 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  44. Quantum Logic.C. de Ronde, and, G. Domenech & H. Freytes - 2016 - Internet Encyclopedia of Philosophy.
    Quantum Logic in Historical and Philosophical Perspective Quantum Logic was developed as an attempt to construct a propositional structure that would allow for describing the events of interest in Quantum Mechanics. QL replaced the Boolean structure, which, although suitable for the discourse of classical physics, was inadequate for representing the atomic realm. The … Continue reading Quantum Logic →.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  45. Modality and Contextuality in Topos Quantum Theory.Benjamin Eva - 2016 - Studia Logica 104 (6):1099-1118.
    Topos quantum theory represents a whole new approach to the formalization of non-relativistic quantum theory. It is well known that TQT replaces the orthomodular quantum logic of the traditional Hilbert space formalism with a new intuitionistic logic that arises naturally from the topos theoretic structure of the theory. However, it is less well known that TQT also has a dual logical structure that is paraconsistent. In this paper, we investigate the relationship between these two logical structures and study the implications (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  46. Quantum logic associated to finite dimensional intervals of modular ortholattices.R. Giuntini, H. Freytes & G. Sergioli - 2016 - Journal of Symbolic Logic 81 (2):629-640.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  47. 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.
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  48. First-order frames for orthomodular quantum logic.Chrysafis Hartonas - 2016 - Journal of Applied Non-Classical Logics 26 (1):69-80.
    One of the main problems of the orthoframe approach to quantum logic was that orthomodularity could not be captured by any first-order condition. This paper studies an elementary and natural class of orthomodular frames that can work around this limitation. Set-theoretically, the frames we propose form a natural subclass of the orthoframes, where is an irreflexive and symmetric relation on X. More specifically, they are partially-ordered orthoframes with a designated subset. Our frame class contains the canonical orthomodular frame of the (...)
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  49. On the Notion of Truth in Quantum Mechanics: A Category-Theoretic Standpoint.Vassilios Karakostas & Elias Zafiris - 2016 - In Diederik Aerts, Christian de Ronde, Hector Freytes & Roberto Giuntini (eds.), Probing the Meaning and Structure of Quantum Mechanics: Semantics, Dynamics and Identity. World Scientific. pp. 1-43.
    The category-theoretic representation of quantum event structures provides a canonical setting for confronting the fundamental problem of truth valua- tion in quantum mechanics as exemplified, in particular, by Kochen-Specker’s theorem. In the present study, this is realized on the basis of the existence of a categorical adjunction between the category of sheaves of variable local Boolean frames, constituting a topos, and the category of quantum event al- gebras. We show explicitly that the latter category is equipped with an object of (...)
    Remove from this list  
     
    Export citation  
     
    Bookmark  
  50. The Intrinsic Quantum Nature of Nash Equilibrium Mixtures.Yohan Pelosse - 2016 - Journal of Philosophical Logic 45 (1):25-64.
    In classical game theory the idea that players randomize between their actions according to a particular optimal probability distribution has always been viewed as puzzling. In this paper, we establish a fundamental connection between n-person normal form games and quantum mechanics, which eliminates the conceptual problems of these random strategies. While the two theories have been regarded as distinct, our main theorem proves that if we do not give any other piece of information to a player in a game, than (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
1 — 50 / 572