Search results for 'Quantum logic' (try it on Scholar)

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  1. Jaakko Hintikka (2002). Quantum Logic as a Fragment of Independence-Friendly Logic. Journal of Philosophical Logic 31 (3):197-209.score: 246.0
    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 (...)
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  2. Kenji Tokuo (2003). Extended Quantum Logic. Journal of Philosophical Logic 32 (5):549-563.score: 246.0
    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.
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  3. Peter Mittelstaedt (2012). Are the Laws of Quantum Logic Laws of Nature? Journal for General Philosophy of Science 43 (2):215-222.score: 240.0
    The main goal of quantum logic is the bottom-up reconstruction of quantum mechanics in Hilbert space. Here we discuss the question whether quantum logic is an empirical structure or a priori valid. There are good reasons for both possibilities. First, with respect to the possibility of a rational reconstruction of quantum mechanics, quantum logic follows a priori from quantum ontology and can thus not be considered as a law of nature. Second, (...)
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  4. Michael Ashcroft (2010). Does Science Influence the Logic We Ought to Use: A Reflection on the Quantum Logic Controversy. Studia Logica 95 (1/2):183 - 206.score: 240.0
    In this article I argue that there is a sense in which logic is empirical, and hence open to influence from science. One of the roles of logic is the modelling and extending of natural language reasoning. It does so by providing a formal system which succeeds in modelling the structure of a paradigmatic set of our natural language inferences and which then permits us to extend this structure to novel cases with relative ease. In choosing the best (...)
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  5. Alexandru Baltag & Sonja Smets (2012). The Dynamic Turn in Quantum Logic. Synthese 186 (3):753 - 773.score: 240.0
    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, (...)
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  6. Jarosław Pykacz (2010). Unification of Two Approaches to Quantum Logic: Every Birkhoff -von Neumann Quantum Logic is a Partial Infinite-Valued Łukasiewicz Logic. Studia Logica 95 (1/2):5 - 20.score: 240.0
    In the paper it is shown that every physically sound Birkhoff - von Neumann quantum logic, i.e., an orthomodular partially ordered set with an ordering set of probability measures can be treated as partial infini te-valued Lukasiewicz logic, which unifies two competing approaches: the many-valued, and the two-valued but non-distributive, which have co-existed in the quantum logic theory since its very beginning.
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  7. Gin McCollum (2002). Systems of Logical Systems: Neuroscience and Quantum Logic. [REVIEW] Foundations of Science 7 (1-2):49-72.score: 240.0
    Nervous systems are intricately organized on many levels of analysis.The intricate organization invites the development of mathematicalsystems that reflect its logical structure. Particular logical structures and choices of invariants within those structures narrowthe ranges of perceptions that are possible and sensorimotorcoordination that may be selected. As in quantum logic, choicesaffect outcomes.Some of the mathematical tools in use in quantum logic havealready also been used in neurobiology, including the mathematicsof ordered structures and a product like a tensor (...)
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  8. Martijn Caspers, Chris Heunen, Nicolaas P. Landsman & Bas Spitters (2009). Intuitionistic Quantum Logic of an N-Level System. Foundations of Physics 39 (7):731-759.score: 240.0
    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 (...)
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  9. Peter Gibbins (1987). Particles and Paradoxes: The Limits of Quantum Logic. Cambridge University Press.score: 240.0
    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 (...)
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  10. Robert B. Griffiths (2014). The New Quantum Logic. Foundations of Physics 44 (6):610-640.score: 240.0
    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 (...)
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  11. Ronnie Hermens (2013). Weakly Intuitionistic Quantum Logic. Studia Logica 101 (5):901-913.score: 240.0
    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 (...)
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  12. Chris Heunen, Nicolaas P. Landsman & Bas Spitters (2012). Bohrification of Operator Algebras and Quantum Logic. Synthese 186 (3):719 - 752.score: 240.0
    Following Birkhoff and von Neumann, quantum logic has traditionally been based on the lattice of closed linear subspaces of some Hubert space, or, more generally, on the lattice of projections in a von Neumann algebra A. Unfortunately, the logical interpretation of these lattices is impaired by their nondistributivity and by various other problems. We show that a possible resolution of these difficulties, suggested by the ideas of Bohr, emerges if instead of single projections one considers elementary propositions to (...)
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  13. Normal D. Megill & Mladen Pavičić (2002). Deduction, Ordering, and Operations in Quantum Logic. Foundations of Physics 32 (3):357-378.score: 240.0
    We show that in quantum logic of closed subspaces of Hilbert space one cannot substitute quantum operations for classical (standard Hilbert space) ones and treat them as primitive operations. We consider two possible ways of such a substitution and arrive at operation algebras that are not lattices what proves the claim. We devise algorithms and programs which write down any two-variable expression in an orthomodular lattice by means of classical and quantum operations in an identical form. (...)
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  14. Alexandru Baltag & Sonja Smets (2011). Quantum Logic as a Dynamic Logic. Synthese 179 (2):285 - 306.score: 240.0
    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 (...)
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  15. Allen Stairs & Jeffrey Bub (2013). Correlations, Contextuality and Quantum Logic. Journal of Philosophical Logic 42 (3):483-499.score: 230.0
    Quantum theory is a probabilistic theory that embodies notoriously striking correlations, stronger than any that classical theories allow but not as strong as those of hypothetical ‘super-quantum’ theories. This raises the question ‘Why the quantum?’—whether there is a handful of principles that account for the character of quantum probability. We ask what quantum-logical notions correspond to this investigation. This project isn’t meant to compete with the many beautiful results that information-theoretic approaches have yielded but rather (...)
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  16. Satoko Titani, Heiji Kodera & Hiroshi Aoyama (2013). Systems of Quantum Logic. Studia Logica 101 (1):193-217.score: 228.0
    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 (...)
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  17. Philip G. Calabrese (2005). Toward a More Natural Expression of Quantum Logic with Boolean Fractions. Journal of Philosophical Logic 34 (4):363 - 401.score: 198.0
    This paper uses a non-distributive system of Boolean fractions (a|b), where a and b are 2-valued propositions or events, to express uncertain conditional propositions and conditional events. These Boolean fractions, 'a if b' or 'a given b', ordered pairs of events, which did not exist for the founders of quantum logic, can better represent uncertain conditional information just as integer fractions can better represent partial distances on a number line. Since the indeterminacy of some pairs of quantum (...)
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  18. Maarten Van den Nest & Hans J. Briegel (2008). Measurement-Based Quantum Computation and Undecidable Logic. Foundations of Physics 38 (5):448-457.score: 192.0
    We establish a connection between measurement-based quantum computation and the field of mathematical logic. We show that the computational power of an important class of quantum states called graph states, representing resources for measurement-based quantum computation, is reflected in the expressive power of (classical) formal logic languages defined on the underlying mathematical graphs. In particular, we show that for all graph state resources which can yield a computational speed-up with respect to classical computation, the underlying (...)
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  19. P. Mittelstaedt & E. -W. Stachow (1978). The Principle of Excluded Middle in Quantum Logic. Journal of Philosophical Logic 7 (1):181 - 208.score: 186.0
    The principle of excluded middle is the logical interpretation of the law V ≤ A v ヿA in an orthocomplemented lattice and, hence, in the lattice of the subspaces of a Hilbert space which correspond to quantum mechanical propositions. We use the dialogic approach to logic in order to show that, in addition to the already established laws of effective quantum logic, the principle of excluded middle can also be founded. The dialogic approach is based on (...)
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  20. Yannis Delmas-Rigoutsos (1997). A Double Deduction System for Quantum Logic Based on Natural Deduction. Journal of Philosophical Logic 26 (1):57-67.score: 186.0
    The author presents a deduction system for Quantum Logic. This system is a combination of a natural deduction system and rules based on the relation of compatibility. This relation is the logical correspondant of the commutativity of observables in Quantum Mechanics or perpendicularity in Hilbert spaces. Contrary to the system proposed by Gibbins and Cutland, the natural deduction part of the system is pure: no algebraic artefact is added. The rules of the system are the rules of (...)
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  21. Miklós Rédei (2007). The Birth of Quantum Logic. History and Philosophy of Logic 28 (2):107-122.score: 186.0
    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 (...)
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  22. Peter Mittelstaedt (1977). Time Dependent Propositions and Quantum Logic. Journal of Philosophical Logic 6 (1):463 - 472.score: 186.0
    Compound propositions which can successfully be defended in a quantumdialogue independent of the elementary propositions contained in it, must have this property also independent of the mutual elementary commensur-abilities. On the other hand, formal commensurabilities must be taken into account. Therefore, for propositions which can be proved by P, irrespective of both the elementary propositions and of the elementary commensur-abilities, there exists a formal strategy of success. The totality of propositions with a formal strategy of success in a quantum (...)
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  23. Sonja Smets (2003). In Defense of Operational Quantum Logic. Logic and Logical Philosophy 11:191-212.score: 186.0
    In the literature the work of C. Piron on OQL, “the operational quantum logic of the Geneva School”, has a few times been criticised. Those criticisms were often due to misunderstandings, as has already been pointed out in [19]. In this paper we follow the line of defense in favour of OQL by replying to the criticisms formulated some time ago in [4] and [17]. In order for the reader to follow our argumentation, we briefly analyze the basic (...)
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  24. E. -W. Stachow (1976). Completeness of Quantum Logic. Journal of Philosophical Logic 5 (2):237 - 280.score: 186.0
    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 (...)
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  25. Othman Qasim Malhas (1987). Quantum Logic and the Classical Propositional Calculus. Journal of Symbolic Logic 52 (3):834-841.score: 186.0
    In much the same way that it is possible to construct a model of hyperbolic geometry in the Euclidean plane, it is possible to model quantum logic within the classical propositional calculus.
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  26. J. L. Bell (1986). A New Approach to Quantum Logic. British Journal for the Philosophy of Science 37 (1):83-99.score: 180.0
    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 (...)
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  27. Sonja Smets (2006). From Intuitionistic Logic to Dynamic Operational Quantum Logic. Poznan Studies in the Philosophy of the Sciences and the Humanities 91 (1):257-275.score: 180.0
    Research within the operational approach to the logical foundations of physics has recently pointed out a new perspective in which quantum logic can be viewed as an intuitionistic logic with an additional operator to capture its essential, i.e., non-distributive, properties. In this paper we will offer an introduction to this approach. We will focus further on why quantum logic has an inherent dynamic nature which is captured in the meaning of "orthomodularity" and on how it (...)
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  28. R. I. G. Hughes (1980). Quantum Logic and the Interpretation of Quantum Mechanics. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1980:55 - 67.score: 180.0
    One problem with assessing quantum logic is that there are considerable differences between its practitioners. In particular they offer different versions of the set of sentences which the logic governs. On some accounts the sentences involved describe events, on others they are ascriptions of properties. In this paper a framework is offered within which to discuss different quantum logical interpretations of quantum theory, and then the works of Jauch, Putnam, van Fraassen and Kochen are located (...)
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  29. Allen Stairs (1983). Quantum Logic, Realism, and Value Definiteness. Philosophy of Science 50 (4):578-602.score: 180.0
    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 (...)
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  30. Geoffrey Hellman (1980). Quantum Logic and Meaning. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1980:493 - 511.score: 180.0
    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 (...)
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  31. Michael Dickson (2001). Quantum Logic is Alive ∧ (It is True ∨ It is False). Proceedings of the Philosophy of Science Association 2001 (3):S274 - S287.score: 180.0
    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 (...)
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  32. John Bell & Michael Hallett (1982). Logic, Quantum Logic and Empiricism. Philosophy of Science 49 (3):355-379.score: 180.0
    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, (...)
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  33. Sławomir Bugajski (1982). What is Quantum Logic? Studia Logica 41 (4):311 - 316.score: 180.0
    The paper describes in detail the procedure of identification of the inner language and an inner logico of a physical theory. The procedure is a generalization of the original ideas of J. von Neuman and G. Birkhoff about quantum logic.
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  34. Claudio Garola & Sandro Sozzo (2013). Recovering Quantum Logic Within an Extended Classical Framework. Erkenntnis 78 (2):399-419.score: 180.0
    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 (...)
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  35. Geoffrey Hellman (1981). Quantum Logic and the Projection Postulate. Philosophy of Science 48 (3):469-486.score: 180.0
    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 (...)
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  36. Bob Coecke (2002). Disjunctive Quantum Logic in Dynamic Perspective. Studia Logica 71 (1):47 - 56.score: 180.0
    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 (...)
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  37. Claudio Garola (1992). Truth Versus Testability in Quantum Logic. Erkenntnis 37 (2):197 - 222.score: 180.0
    We forward an epistemological perspective regarding non-classical logics which restores the universality of logic in accordance with the thesis of global pluralism. In this perspective every non-classical truth-theory is actually a theory of some metalinguistic concept which does not coincide with the concept of truth (described by Tarski's truth theory). We intend to apply this point of view to Quantum Logic (QL) in order to prove that its structure properties derive from properties of the metalinguistic concept of (...)
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  38. Itamar Pitowsky (1982). Substitution and Truth in Quantum Logic. Philosophy of Science 49 (3):380-401.score: 180.0
    If p(x 1 ,...,x n ) and q(x 1 ,...,x n ) are two logically equivalent propositions then p(π (x 1 ),...,π (x n )) and q(π (x 1 ),...,π (x n )) are also logically equivalent where π is an arbitrary permutation of the elementary constituents x 1 ,...,x n . In Quantum Logic the invariance of logical equivalences breaks down. It is proved that the distribution rules of classical logic are in fact equivalent to the (...)
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  39. Allen Stairs (1982). Quantum Logic and the Luders Rule. Philosophy of Science 49 (3):422-436.score: 180.0
    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 (...)
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  40. J. L. Bell (1985). Orthospaces and Quantum Logic. Foundations of Physics 15 (12):1179-1202.score: 180.0
    In this paper we construct the ortholattices arising in quantum logic starting from the phenomenologically plausible idea of a collection of ensembles subject to passing or failing various “tests.” A collection of ensembles forms a certain kind of preordered set with extra structure called anorthospace; we show that complete ortholattices arise as canonical completions of orthospaces in much the same way as arbitrary complete lattices arise as canonical completions of partially ordered sets. We also show that the canonical (...)
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  41. Sonja Smets, On Causation and a Counterfactual in Quantum Logic: The Sasaki Hook.score: 180.0
    We analyze G.M. Hardegree's interpretation of the Sasaki hook as a Stalnaker conditional and explain how he makes use of the basic conceptual machinery of OQL, i.e. the operational quantum logic which originated with the Geneva Approach to the foundations of physics. In particular we focus on measurements which are ideal and of the first kind, since these encode the content of the so-called Sasaki projections within the Geneva Approach. The Sasaki projections play a fundamental role when analyzing (...)
     
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  42. T. A. Brody (1984). On Quantum Logic. Foundations of Physics 14 (5):409-430.score: 180.0
    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 (...)
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  43. Jan Broekaert & Bart D'Hooghe (2000). A Model with Quantum Logic, but Non-Quantum Probability: The Product Test Issue. [REVIEW] Foundations of Physics 30 (9):1481-1501.score: 180.0
    We introduce a model with a set of experiments of which the probabilities of the outcomes coincide with the quantum probabilities for the spin measurements of a quantum spin- $ \frac{1}{2} $ particle. Product tests are defined which allow simultaneous measurements of incompatible observables, which leads to a discussion of the validity of the meet of two propositions as the algebraic model for conjunction in quantum logic. Although the entity possesses the same structure for the (...) of its experimental propositions as a genuine spin- $ \frac{1}{2} $ quantum entity, the probability measure corresponding with the meet of propositions using the Hilbert space representation and quantum rules does not render the probability of the conjunction of the two propositions. Accordingly, some fundamental concepts of quantum logic, Piron-products, “classical” systems and the general problem of hidden variable theories for quantum theory are discussed. (shrink)
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  44. Patrick A. Heelan (1970). Complementarity, Context Dependence, and Quantum Logic. Foundations of Physics 1 (2):95-110.score: 180.0
    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.
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  45. Bart Jacobs & Jorik Mandemaker (2012). Coreflections in Algebraic Quantum Logic. Foundations of Physics 42 (7):932-958.score: 180.0
    Various generalizations of Boolean algebras are being studied in algebraic quantum logic, including orthomodular lattices, orthomodular po-sets, orthoalgebras and effect algebras. This paper contains a systematic study of the structure in and between categories of such algebras. It does so via a combination of totalization (of partially defined operations) and transfer of structure via coreflections.
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  46. P. Mittelstaedt & E. W. Stachow (1974). Operational Foundation of Quantum Logic. Foundations of Physics 4 (3):355-365.score: 180.0
    The logic of quantum mechanical propositions—called quantum logic—is constructed on the basis of the operational foundation of logic. Some obvious modifications of the operational method, which come from the incommensurability of the quantum mechanical propositions, lead to the effective quantum logic. It is shown in this paper that in the framework of a calculization of this effective quantum logic the negation of a proposition is uniquely defined (Theorem I), and that (...)
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  47. Carl A. Hein (1979). Entropy in Operational Statistics and Quantum Logic. Foundations of Physics 9 (9-10):751-786.score: 180.0
    In a series of recent papers, Randall and Foulis have developed a generalized theory of probability (operational statistics) which is based on the notion of a physical operation. They have shown that the quantum logic description of quantum mechanics can be naturally imbedded into this generalized theory of probability. In this paper we shall investigate the role of entropy (in the sense of Shannon's theory of information) in operational statistics. We shall find that there are several related (...)
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  48. Mladen Pavičić (1989). Unified Quantum Logic. Foundations of Physics 19 (8):999-1016.score: 180.0
    Unified quantum logic based on unified operations of implication is formulated as an axiomatic calculus. Soundness and completeness are demonstrated using standard algebraic techniques. An embedding of quantum logic into a new modal system is carried out and discussed.
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  49. Peter Mittelstaedt (1978). The Metalogic of Quantum Logic. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1978:249 - 256.score: 176.0
    The logic of quantum physical propositions can be established by means of dialogs which take account of the general incommensurability of these propositions. Investigated first are meta-propositions which state the formal truth of object-propositions. It turns out that the logic of these meta-propositions is equivalent to ordinary logic. A special class of meta-propositions which state the material truth of object-propositions may be considered as quantum logical modalities. It is found that the logic of these (...)
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  50. N. Da Costa & C. De Ronde (2013). The Paraconsistent Logic of Quantum Superpositions. Foundations of Physics 43 (7):845-858.score: 174.0
    Physical superpositions exist both in classical and in quantum physics. However, what is exactly meant by ‘superposition’ in each case is extremely different. In this paper we discuss some of the multiple interpretations which exist in the literature regarding superpositions in quantum mechanics. We argue that all these interpretations have something in common: they all attempt to avoid ‘contradiction’. We argue in this paper, in favor of the importance of developing a new interpretation of superpositions which takes into (...)
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