Results for 'quantum logic'

1000+ found
Order:
See also
  1.  27
    Quantum Logic and Probability Theory.Alexander Wilce - 2008 - Stanford Encyclopedia of Philosophy.
    Direct download  
     
    Export citation  
     
    Bookmark   9 citations  
  2.  37
    Extended Quantum Logic.Kenji Tokuo - 2003 - Journal of Philosophical Logic 32 (5):549-563.
    The concept of quantum logic is extended so that it covers a more general set of propositions that involve non-trivial probabilities. This structure is shown to be embedded into a multi-modal framework, which has desirable logical properties such as an axiomatization, the finite model property and decidability.
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  3.  93
    Quantum Logic as a Dynamic Logic.Alexandru Baltag & Sonja Smets - 2011 - Synthese 179 (2):285 - 306.
    We address the old question whether a logical understanding of Quantum Mechanics requires abandoning some of the principles of classical logic. Against Putnam and others (Among whom we may count or not E. W. Beth, depending on how we interpret some of his statements), our answer is a clear "no". Philosophically, our argument is based on combining a formal semantic approach, in the spirit of E. W. Beth's proposal of applying Tarski's semantical methods to the analysis of physical (...)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   10 citations  
  4.  23
    Quantum Logic.Peter Mittelstaedt - 1974 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1974 (2):501 - 514.
    Direct download  
     
    Export citation  
     
    Bookmark   34 citations  
  5. Quantum Logic, Realism, and Value Definiteness.Allen Stairs - 1983 - Philosophy of Science 50 (4):578-602.
    One of the most interesting programs in the foundations of quantum mechanics is the realist quantum logic approach associated with Putnam, Bub, Demopoulos and Friedman (and which is the focus of my own research.) I believe that realist quantum logic is our best hope for making sense of quantum mechanics, but I have come to suspect that the usual version may not be the correct one. In this paper, I would like to say why (...)
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   32 citations  
  6. 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 (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  7.  77
    Intuitionistic Quantum Logic of an N-Level System.Martijn Caspers, Chris Heunen, Nicolaas P. Landsman & Bas Spitters - 2009 - Foundations of Physics 39 (7):731-759.
    A decade ago, Isham and Butterfield proposed a topos-theoretic approach to quantum mechanics, which meanwhile has been extended by Döring and Isham so as to provide a new mathematical foundation for all of physics. Last year, three of the present authors redeveloped and refined these ideas by combining the C*-algebraic approach to quantum theory with the so-called internal language of topos theory (Heunen et al. in arXiv:0709.4364). The goal of the present paper is to illustrate our abstract setup (...)
    Direct download (12 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  8. Quantum Logic is Alive ∧ (It is True ∨ It is False).Michael Dickson - 2001 - Proceedings of the Philosophy of Science Association 2001 (3):S274 - S287.
    Is the quantum-logic interpretation dead? Its near total absence from current discussions about the interpretation of quantum theory suggests so. While mathematical work on quantum logic continues largely unabated, interest in the quantum-logic interpretation seems to be almost nil, at least in Anglo-American philosophy of physics. This paper has the immodest purpose of changing that fact. I shall argue that while the quantum-logic interpretation faces challenges, it remains a live option. The (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   9 citations  
  9.  5
    Quantum Logic and the Unity of Science.John Woods & Kent A. Peacock - 2004 - In S. Rahman J. Symons (ed.), Logic, Epistemology, and the Unity of Science. Kluwer Academic Publisher. pp. 257--287.
  10. Quantum Logic as a Fragment of Independence-Friendly Logic.Jaakko Hintikka - 2002 - Journal of Philosophical Logic 31 (3):197-209.
    The working assumption of this paper is that noncommuting variables are irreducibly interdependent. The logic of such dependence relations is the author's independence-friendly (IF) logic, extended by adding to it sentence-initial contradictory negation ¬ over and above the dual (strong) negation ∼. Then in a Hilbert space ∼ turns out to express orthocomplementation. This can be extended to any logical space, which makes it possible to define the dimension of a logical space. The received Birkhoff and von Neumann (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  11. Is Quantum Logic Really Logic?Michael R. Gardner - 1971 - Philosophy of Science 38 (4):508-529.
    Putnam and Finkelstein have proposed the abandonment of distributivity in the logic of quantum theory. This change results from defining the connectives, not truth-functionally, but in terms of a certain empirical ordering of propositions. Putnam has argued that the use of this ordering ("implication") to govern proofs resolves certain paradoxes. But his resolutions are faulty; and in any case, the paradoxes may be resolved with no changes in logic. There is therefore no reason to regard the partially (...)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   11 citations  
  12.  2
    Quantum Logic in Algebraic Approach.K. Svozil - 2001 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 32 (1):113-115.
  13. A New Approach to Quantum Logic.J. L. Bell - 1986 - British Journal for the Philosophy of Science 37 (1):83-99.
    The idea of a 'logic of quantum mechanics' or quantum logic was originally suggested by Birkhoff and von Neumann in their pioneering paper [1936]. Since that time there has been much argument about whether, or in what sense, quantum 'logic' can be actually considered a true logic (see, e.g. Bell and Hallett [1982], Dummett [1976], Gardner [1971]) and, if so, how it is to be distinguished from classical logic. In this paper I (...)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   46 citations  
  14. Logic, Quantum Logic and Empiricism.John Bell & Michael Hallett - 1982 - Philosophy of Science 49 (3):355-379.
    This paper treats some of the issues raised by Putnam's discussion of, and claims for, quantum logic, specifically: that its proposal is a response to experimental difficulties; that it is a reasonable replacement for classical logic because its connectives retain their classical meanings, and because it can be derived as a logic of tests. We argue that the first claim is wrong (1), and that while conjunction and disjunction can be considered to retain their classical meanings, (...)
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  15.  10
    Quantum Logic Is Alive ∧.Michael Dickson - 2001 - Philosophy of Science 68 (3):274-287.
    Is the quantum-logic interpretation dead? Its near total absence from current discussions about the interpretation of quantum theory suggests so. While mathematical work on quantum logic continues largely unabated, interest in the quantum-logic interpretation seems to be almost nil, at least in Anglo-American philosophy of physics. This paper has the immodest purpose of changing that fact. I shall argue that while the quantum-logic interpretation faces challenges, it remains a live option. The (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  16.  46
    Recovering Quantum Logic Within an Extended Classical Framework.Claudio Garola & Sandro Sozzo - 2013 - Erkenntnis 78 (2):399-419.
    We present a procedure which allows us to recover classical and nonclassical logical structures as concrete logics associated with physical theories expressed by means of classical languages. This procedure consists in choosing, for a given theory ${{\mathcal{T}}}$ and classical language ${{\fancyscript{L}}}$ expressing ${{\mathcal{T}}, }$ an observative sublanguage L of ${{\fancyscript{L}}}$ with a notion of truth as correspondence, introducing in L a derived and theory-dependent notion of C-truth (true with certainty), defining a physical preorder $\prec$ induced by C-truth, and finally selecting (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  17. The Dynamic Turn in Quantum Logic.Alexandru Baltag & Sonja Smets - 2012 - Synthese 186 (3):753 - 773.
    In this paper we show how ideas coming from two areas of research in logic can reinforce each other. The first such line of inquiry concerns the "dynamic turn" in logic and especially the formalisms inspired by Propositional Dynamic Logic (PDL); while the second line concerns research into the logical foundations of Quantum Physics, and in particular the area known as Operational Quantum Logic, as developed by Jauch and Piron (Helve Phys Acta 42: 842-848, (...)
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  18.  53
    Quantum Logic and Physical Modalities.M. L. Dalla Chiara - 1977 - Journal of Philosophical Logic 6 (1):391-404.
  19.  47
    Quantum Logic and the Luders Rule.Allen Stairs - 1982 - Philosophy of Science 49 (3):422-436.
    In a recent paper, Michael Friedman and Hilary Putnam argued that the Luders rule is ad hoc from the point of view of the Copenhagen interpretation but that it receives a natural explanation within realist quantum logic as a probability conditionalization rule. Geoffrey Hellman maintains that quantum logic cannot give a non-circular explanation of the rule, while Jeffrey Bub argues that the rule is not ad hoc within the Copenhagen interpretation. As I see it, all four (...)
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  20.  43
    A Quantum Logic of Down Below.Peter D. Bruza, Dominic Widdows & John Woods - unknown
    This chapter is offered as a contribution to the logic of down below. We attempt to demonstrate that the nature of human agency necessitates that there actually be such a logic. The ensuing sections develop the suggestion that cognition down below has a structure strikingly similar to the physical structure of quantum states. In its general form, this is not an idea that originates with the present authors. It is known that there exist mathematical models from the (...)
    Direct download  
     
    Export citation  
     
    Bookmark   3 citations  
  21. Quantum Logic in Intuitionistic Perspective.Bob Coecke - 2002 - Studia Logica 70 (3):411-440.
    In their seminal paper Birkhoff and von Neumann revealed the following dilemma:[ ] whereas for logicians the orthocomplementation properties of negation were the ones least able to withstand a critical analysis, the study of mechanics points to the distributive identities as the weakest link in the algebra of logic.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  22.  29
    Quantum Logic, Conditional Probability, and Interference.Michael Friedman & Hilary Putnam - 1978 - Dialectica 32 (3‐4):305-315.
  23.  76
    Quantum Logic as Motivated by Quantum Computing.J. Michael Dunn, Tobias J. Hagge, Lawrence S. Moss & Zhenghan Wang - 2005 - Journal of Symbolic Logic 70 (2):353 - 359.
  24.  99
    The New Quantum Logic.Robert B. Griffiths - 2014 - Foundations of Physics 44 (6):610-640.
    It is shown how all the major conceptual difficulties of standard (textbook) quantum mechanics, including the two measurement problems and the (supposed) nonlocality that conflicts with special relativity, are resolved in the consistent or decoherent histories interpretation of quantum mechanics by using a modified form of quantum logic to discuss quantum properties (subspaces of the quantum Hilbert space), and treating quantum time development as a stochastic process. The histories approach in turn gives rise (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  25. Quantum Information Processing, Operational Quantum Logic, Convexity, and the Foundations of Physics.Howard Barnum - 2003 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 34 (3):343-379.
    Quantum information science is a source of task-related axioms whose consequences can be explored in general settings encompassing quantum mechanics, classical theory, and more. Quantum states are compendia of probabilities for the outcomes of possible operations we may perform on a system: ''operational states.'' I discuss general frameworks for ''operational theories'' (sets of possible operational states of a system), in which convexity plays key role. The main technical content of the paper is in a theorem that any (...)
    Direct download (11 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  26.  21
    Proof Theory of Paraconsistent Quantum Logic.Norihiro Kamide - 2018 - Journal of Philosophical Logic 47 (2):301-324.
    Paraconsistent quantum logic, a hybrid of minimal quantum logic and paraconsistent four-valued logic, is introduced as Gentzen-type sequent calculi, and the cut-elimination theorems for these calculi are proved. This logic is shown to be decidable through the use of these calculi. A first-order extension of this logic is also shown to be decidable. The relationship between minimal quantum logic and paraconsistent four-valued logic is clarified, and a survey of existing Gentzen-type (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  27.  6
    Quantum Logic.Peter Mittelstaedt - 1980 - Philosophy of Science 47 (2):332-335.
    Direct download  
     
    Export citation  
     
    Bookmark   10 citations  
  28.  46
    Quantum Logic, Conditional Probability, and Interference.Jeffrey Bub - 1982 - Philosophy of Science 49 (3):402-421.
    Friedman and Putnam have argued (Friedman and Putnam 1978) that the quantum logical interpretation of quantum mechanics gives us an explanation of interference that the Copenhagen interpretation cannot supply without invoking an additional ad hoc principle, the projection postulate. I show that it is possible to define a notion of equivalence of experimental arrangements relative to a pure state φ , or (correspondingly) equivalence of Boolean subalgebras in the partial Boolean algebra of projection operators of a system, which (...)
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  29.  66
    Quantum Logic and Meaning.Geoffrey Hellman - 1980 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1980:493 - 511.
    Quantum logic as genuine non-classical logic provides no solution to the "paradoxes" of quantum mechanics. From the minimal condition that synonyms be substitutable salva veritate, it follows that synonymous sentential connectives be alike in point of truth-functionality. It is a fact of pure mathematics that any assignment Φ of (0, 1) to the subspaces of Hilbert space (dim. ≥ 3) which guarantees truth-preservation of the ordering and truth-functionality of QL negation, violates truth-functionality of QL ∨ and (...)
    Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  30.  9
    Quantum Logic and Non-Separability.Bernard D'Espagnat - 1973 - In Jagdish Mehra (ed.), The Physicist's Conception of Nature. Boston: Reidel. pp. 714--735.
    Direct download  
     
    Export citation  
     
    Bookmark   5 citations  
  31.  12
    Quantum Logic in Algebraic Approach.K. Svozil - 2001 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 32 (1):113-115.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  32. Quantum Logic and Quantum Probability.A. Wilce - forthcoming - Stanford Encyclopedia of Philosophy.
     
    Export citation  
     
    Bookmark   1 citation  
  33.  9
    Quantum Logic Properties of Hypergraphs.Matthias P. Kläy - 1987 - Foundations of Physics 17 (10):1019-1036.
    In quantum logics, the notions of strong and full order determination and unitality for states on orthomodular posets are well known. These notions are defined for hypergraphs and their state spaces in a consistent manner and the relations between them and to the notions defined for orthomodular posets are discussed. The state space of a hypergraph is a polytope. This polytope is a simplex if and only if every superposition of pure states is a mixture of these same pure (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  34.  13
    Quantum Information Processing, Operational Quantum Logic, Convexity, and the Foundations of Physics.Howard Barnum - 2003 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 34 (3):343-379.
  35. The Quantum Logic of Zeno: Misconceptions and Restorations.Constantin Antonopoulos - 2007 - Acta Philosophica 16 (2):265-284.
  36.  59
    Quantum Logic Is Alive [Logical And] (It Is True [Logical Or] It Is False).Michael Dickson - 2001 - Philosophy of Science 68 (S1):S274-.
    Is the quantum-logic interpretation dead? Its near total absence from current discussions about the interpretation of quantum theory suggests so. While mathematical work on quantum logic continues largely unabated, interest in the quantum-logic interpretation seems to be almost nil, at least in Anglo-American philosophy of physics. This paper has the immodest purpose of changing that fact. I shall argue that while the quantum-logic interpretation faces challenges, it remains a live option. The (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  37.  43
    Disjunctive Quantum Logic in Dynamic Perspective.Bob Coecke - 2002 - Studia Logica 71 (1):47 - 56.
    In Coecke (2002) we proposed the intuitionistic or disjunctive representation of quantum logic, i.e., a representation of the property lattice of physical systems as a complete Heyting algebra of logical propositions on these properties, where this complete Heyting algebra goes equipped with an additional operation, the operational resolution, which identifies the properties within the logic of propositions. This representation has an important application towards dynamic quantum logic, namely in describing the temporal indeterministic propagation of actual (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  38.  16
    Primacy of Quantum Logic in the Natural World.Cynthia Sue Larson - 2015 - Cosmos and History 11 (2):326-340.
    72 1024x768 This paper presents evidence from the fields of cognitive science and quantum information theory suggesting quantum theory to be the dominant fundamental logic in the natural world, in direct challenge to the long-held assumption that quantum logic only need be considered ‘in the quantum realm.' A summary of the evolution of quantum logic and quantum theory is presented, along with an overview for the necessity of incomplete quantum knowledge, (...)
    Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  39.  36
    On Quantum Logic.T. A. Brody - 1984 - Foundations of Physics 14 (5):409-430.
    The status and justification of quantum logic are reviewed. On the basis of several independent arguments it is concluded that it cannot be a logic in the philosophical sense of a general theory concerning the structure of valid inferences. Taken as a calculus for combining quantum mechanical propositions, it leaves a number of significant aspects of quantum physics unaccounted for. It is shown, moreover, that quantum logic, far from being more general than Boolean (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  40.  56
    Particles and Paradoxes: The Limits of Quantum Logic.Peter Gibbins - 1987 - Cambridge University Press.
    Quantum theory is our deepest theory of the nature of matter. It is a theory that, notoriously, produces results which challenge the laws of classical logic and suggests that the physical world is illogical. This book gives a critical review of work on the foundations of quantum mechanics at a level accessible to non-experts. Assuming his readers have some background in mathematics and physics, Peter Gibbins focuses on the questions of whether the results of quantum theory (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   20 citations  
  41.  6
    Disjunctive Quantum Logic in Dynamic Perspective.Bob Coecke - 2002 - Studia Logica 71 (1):47-56.
    In Coecke we proposed the intuitionistic or disjunctive representation of quantum logic, i.e., a representation of the property lattice of physical systems as a complete Heyting algebra of logical propositions on these properties, where this complete Heyting algebra goes equipped with an additional operation, the operational resolution, which identifies the properties within the logic of propositions. This representation has an important application "towards dynamic quantum logic", namely in describing the temporal indeterministic propagation of actual properties (...)
    Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  42.  32
    Weakly Intuitionistic Quantum Logic.Ronnie Hermens - 2013 - Studia Logica 101 (5):901-913.
    In this article von Neumann’s proposal that in quantum mechanics projections can be seen as propositions is followed. However, the quantum logic derived by Birkhoff and von Neumann is rejected due to the failure of the law of distributivity. The options for constructing a distributive logic while adhering to von Neumann’s proposal are investigated. This is done by rejecting the converse of the proposal, namely, that propositions can always be seen as projections. The result is a (...)
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  43.  28
    Complementarity, Context Dependence, and Quantum Logic.Patrick A. Heelan - 1970 - Foundations of Physics 1 (2):95-110.
    Quantum-mechanical event descriptions are context-dependent descriptions. The role of quantum (nondistributive) logic is in the partial ordering of contexts rather than in the ordering of quantum-mechanical events. Moreover, the kind of quantum logic displayed by quantum mechanics can be easily inferred from the general notion of contextuality used in ordinary language. The formalizable core of Bohr's notion of complementarity is the type of context dependence discussed in this paper.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   10 citations  
  44.  30
    Quantum Logic and the Projection Postulate.Geoffrey Hellman - 1981 - Philosophy of Science 48 (3):469-486.
    This paper explores the status of the von Neumann-Luders state transition rule (the "projection postulate") within "real-logic" quantum logic. The entire discussion proceeds from a reading of the Luders rule according to which, although idealized in applying only to "minimally disturbing" measurements, it nevertheless makes empirical claims and is not a purely mathematical theorem. An argument (due to Friedman and Putnam) is examined to the effect that QL has an explanatory advantage over Copenhagen and other interpretations which (...)
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  45.  8
    Quantum Logic as Motivated by Quantum Computing.J. Michael Dunn, Tobias J. Hagge, Lawrence S. Moss & Zhenghan Wang - 2005 - Journal of Symbolic Logic 70 (2):353-359.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  46.  1
    Quantum Logic, Hilbert Space, Revision Theory.Kurt Engesser & Dov M. Gabbay - 2002 - Artificial Intelligence 136 (1):61-100.
  47.  43
    Systems of Quantum Logic.Satoko Titani, Heiji Kodera & Hiroshi Aoyama - 2013 - Studia Logica 101 (1):193-217.
    Logical implications are closely related to modal operators. Lattice-valued logic LL and quantum logic QL were formulated in Titani S (1999) Lattice Valued Set Theory. Arch Math Logic 38:395–421, Titani S (2009) A Completeness Theorem of Quantum Set Theory. In: Engesser K, Gabbay DM, Lehmann D (eds) Handbook of Quantum Logic and Quantum Structures: Quantum Logic. Elsevier Science Ltd., pp. 661–702, by introducing the basic implication → which represents the lattice (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  48.  9
    Quantum Logic with Implication.J. Jay Zeman - 1979 - Notre Dame Journal of Formal Logic 20 (4):723-728.
  49.  50
    Completeness of Quantum Logic.E. -W. Stachow - 1976 - Journal of Philosophical Logic 5 (2):237 - 280.
    This paper is based on a semantic foundation of quantum logic which makes use of dialog-games. In the first part of the paper the dialogic method is introduced and under the conditions of quantum mechanical measurements the rules of a dialog-game about quantum mechanical propositions are established. In the second part of the paper the quantum mechanical dialog-game is replaced by a calculus of quantum logic. As the main part of the paper we (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  50.  36
    The Birth of Quantum Logic.Miklós Rédei - 2007 - History and Philosophy of Logic 28 (2):107-122.
    By quoting extensively from unpublished letters written by John von Neumann to Garret Birkhoff during the preparatory phase (in 1935) of their ground-breaking 1936 paper that established quantum logic, the main steps in the thought process leading to the 1936 Birkhoff?von Neumann paper are reconstructed. The reconstruction makes it clear why Birkhoff and von Neumann rejected the notion of quantum logic as the projection lattice of an infinite dimensional complex Hilbert space and why they postulated in (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   4 citations  
1 — 50 / 1000