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  1. Andrew Aberdein & Stephen Read (2009). The Philosophy of Alternative Logics. In Leila Haaparanta (ed.), The Development of Modern Logic. Oxford University Press. pp. 613-723.
    This chapter focuses on alternative logics. It discusses a hierarchy of logical reform. It presents case studies that illustrate particular aspects of the logical revisionism discussed in the chapter. The first case study is of intuitionistic logic. The second case study turns to quantum logic, a system proposed on empirical grounds as a resolution of the antinomies of quantum mechanics. The third case study is concerned with systems of relevance logic, which have been the subject of an especially detailed reform (...)
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  2. Samson Abramsky (2013). Relational Hidden Variables and Non-Locality. Studia Logica 101 (2):411-452.
    We use a simple relational framework to develop the key notions and results on hidden variables and non-locality. The extensive literature on these topics in the foundations of quantum mechanics is couched in terms of probabilistic models, and properties such as locality and no-signalling are formulated probabilistically. We show that to a remarkable extent, the main structure of the theory, through the major No-Go theorems and beyond, survives intact under the replacement of probability distributions by mere relations.
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  3. T. Acton, S. Caffrey, S. Dunn, P. Vinson & K. Svozil (1998). Analogues of Quantum Complementarity in the Theory of Automata - a Prolegomenon to the Philosophy of Quantum Mechanics. Studies in History and Philosophy of Science Part B 29 (1):61-80.
    Complementarity is not only a feature of quantum mechanical systems but occurs also in the context of finite automata.
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  4. Diederik Aerts (2013). La mecánica cuántica y la conceptualidad: materia, historias, semántica y espacio-tiempo. Scientiae Studia 11 (1):75-99.
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  5. Diederik Aerts, Ellie D'Hondt & Liane Gabora (2000). Why the Disjunction in Quantum Logic is Not Classical. Foundations of Physics 30 (9):1473-1480.
    The quantum logical `or' is analyzed from a physical perspective. We show that it is the existence of EPR-like correlation states for the quantum mechanical entity under consideration that make it nonequivalent to the classical situation. Specifically, the presence of potentiality in these correlation states gives rise to the quantum deviation from the classical logical `or'. We show how this arises not only in the microworld, but also in macroscopic situations where EPR-like correlation states are present. We investigate how application (...)
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  6. James Aken (1986). Analysis of Quantum Probability Theory. II. Journal of Philosophical Logic 15 (3):333 - 367.
  7. James Aken (1985). Analysis of Quantum Probability Theory. I. Journal of Philosophical Logic 14 (3):267 - 296.
  8. J. Almog (1978). Perhaps (?), New logical foundations are needed for quantum mechanics. Logique Et Analyse 21 (82):251.
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  9. Constantin Antonopoulos (2007). The Quantum Logic of Zeno: Misconceptions and Restorations. Acta Philosophica 16 (2):265-284.
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  10. Hiroshi Aoyama (2004). LK, LJ, Dual Intuitionistic Logic, and Quantum Logic. Notre Dame Journal of Formal Logic 45 (4):193-213.
    In this paper, we study the relationship among classical logic, intuitionistic logic, and quantum logic . These logics are related in an interesting way and are not far apart from each other, as is widely believed. The results in this paper show how they are related with each other through a dual intuitionistic logic . Our study is completely syntactical.
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  11. K. O. Apel (1979). AA. W., The Logico Algebraic Approach to Quantum Mechanics, voL II: Con-Temporary Consolidation, Ed. By CA. Hooker, D. Reidel Publ. Camp., Dor-Drecht-Boston-London, 1979. AA. W., Theoretical Approaches to Complex Systems, Proceedings, Tubingen 1977, Lecture Notes in Biomathematics, 21, Springer-Veriag, Berlin 1978. [REVIEW] International Logic Review 12 (19-24):156.
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  12. 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.
    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 system of (...)
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  13. A. Attanasi, A. Cavagna & J. Lorenzana (2007). Elasticity and Metastability Limit in Supercooled Liquids: A Lattice Model. Philosophical Magazine 87 (3-5):441-448.
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  14. Iep Author (2016). Quantum Logic.
    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 →.
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  15. Guido Bacciagaluppi, Is Logic Empirical?
    The philosophical debate about quantum logic between the late 1960s and the early 1980s was generated mainly by Putnam's claims that quantum mechanics empirically motivates introducing a new form of logic, that such an empirically founded quantum logic is the `true' logic, and that adopting quantum logic would resolve all the paradoxes of quantum mechanics. Most of that debate focussed on the latter claim, reaching the conclusion that it was mistaken. This chapter will attempt to clarify the possible misunderstandings surrounding (...)
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  16. I. C. Baianu (2006). Robert Rosen's Work and Complex Systems Biology. Axiomathes 16 (1-2):25-34.
    Complex Systems Biology approaches are here considered from the viewpoint of Robert Rosen’s (M,R)-systems, Relational Biology and Quantum theory, as well as from the standpoint of computer modeling. Realizability and Entailment of (M,R)-systems are two key aspects that relate the abstract, mathematical world of organizational structure introduced by Rosen to the various physicochemical structures of complex biological systems. Their importance for understanding biological function and life itself, as well as for designing new strategies for treating diseases such as cancers, is (...)
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  17. I. C. Baianu, R. Brown, G. Georgescu & J. F. Glazebrook (2006). Complex Non-Linear Biodynamics in Categories, Higher Dimensional Algebra and Łukasiewicz–Moisil Topos: Transformations of Neuronal, Genetic and Neoplastic Networks. [REVIEW] Axiomathes 16 (1-2):65-122.
    A categorical, higher dimensional algebra and generalized topos framework for Łukasiewicz–Moisil Algebraic–Logic models of non-linear dynamics in complex functional genomes and cell interactomes is proposed. Łukasiewicz–Moisil Algebraic–Logic models of neural, genetic and neoplastic cell networks, as well as signaling pathways in cells are formulated in terms of non-linear dynamic systems with n-state components that allow for the generalization of previous logical models of both genetic activities and neural networks. An algebraic formulation of variable ‘next-state functions’ is extended to a Łukasiewicz–Moisil (...)
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  18. A. Baltag & S. Smets (2008). A Dynamic-Logical Perspective on Quantum Behavior. Studia Logica 89 (2):187-211.
    In this paper we show how recent concepts from Dynamic Logic, and in particular from Dynamic Epistemic logic, can be used to model and interpret quantum behavior. Our main thesis is that all the non-classical properties of quantum systems are explainable in terms of the non-classical flow of quantum information. We give a logical analysis of quantum measurements (formalized using modal operators) as triggers for quantum information flow, and we compare them with other logical operators previously used to model various (...)
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  19. Alexandru Baltag & Sonja Smets (forthcoming). Logics of Informational Interactions. Journal of Philosophical Logic:1-13.
    The pre-eminence of logical dynamics, over a static and purely propositional view of Logic, lies at the core of a new understanding of both formal epistemology and the logical foundations of quantum mechanics. Both areas appear at first sight to be based on purely static propositional formalisms, but in our view their fundamental operators are essentially dynamic in nature. Quantum logic can be best understood as the logic of physically-constrained informational interactions between subsystems of a global physical system. Similarly, epistemic (...)
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  20. Alexandru Baltag & Sonja Smets (2012). The Dynamic Turn in Quantum Logic. 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, 1969), Pirón (Foundations of Quantum Physics, (...)
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  21. Alexandru Baltag & Sonja Smets (2011). Quantum Logic as a Dynamic Logic. 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 theories, with (...)
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  22. Alexandru Baltag & Sonja Smets, The Logic of Quantum Programs.
    We present a logical calculus for reasoning about information flow in quantum programs. In particular we introduce a dynamic logic that is capable of dealing with quantum measurements, unitary evolutions and entanglements in compound quantum systems. We give a syntax and a relational semantics in which we abstract away from phases and probabilities. We present a sound proof system for this logic, and we show how to characterize by logical means various forms of entanglement (e.g. the Bell states) and various (...)
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  23. H. Barnum (2003). Quantum Information Processing, Operational Quantum Logic, Convexity, and the Foundations of Physics. Studies in History and Philosophy of Science Part B 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 such theory naturally (...)
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  24. J. L. Bell (1986). A New Approach to Quantum Logic. 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 put forward a simple and natural semantical framework (...)
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  25. J. L. Bell (1985). Orthospaces and Quantum Logic. Foundations of Physics 15 (12):1179-1202.
    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 completion of (...)
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  26. John Bell & Michael Hallett (1982). Logic, Quantum Logic and Empiricism. 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, negation crucially does not. (...)
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  27. E. G. Beltrametti & G. Cassinelli (1977). On State Transformations Induced by Yes-No Experiments, in the Context of Quantum Logic. Journal of Philosophical Logic 6 (1):369 - 379.
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  28. E. G. Beltrametti & G. Cassinelli (1972). Quantum Mechanics Andp-Adic Numbers. Foundations of Physics 2 (1):1-7.
    We study the possibility of representing the proposition lattice associated with a quantum system by a linear vector space with coefficients from ap-adic field. We find inconsistencies if the lattice is assumed, as usual, to be irreducible, complete, orthocomplemented, atomic, and weakly modular.
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  29. Enrico G. Beltrametti & Bas C. Van Fraassen (1981). Current Issues in Quantum Logic.
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  30. Evert Beth (1940). Strauss M.. Formal Problems of Probability Theory in the Light of Quantum Mechanics Unity of Science Forum, 12 1938, Pp. 35–40; February 1939, Pp. 49–54; April 1939' Pp. 85–72. [REVIEW] Journal of Symbolic Logic 5 (2):72-73.
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  31. Erhard Bieberich, What the Liar Paradox Can Reveal About the Structure of Our Minds.
    In human consciousness perceptions are distinct or atomistic events despite being perceived by an apparently undivided inner observer. This paper applies both classical (Boolean) and quantum logic to analysis of the Liar paradox which is taken as a typical example of a self-referential negation in the perception space of an undivided observer. The conception of self-referential paradoxes is a unique ability of the human mind still lacking an explanation on the basis of logic. It will be shown that both classical (...)
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  32. Tomasz Bigaj (2001). Three-Valued Logic, Indeterminacy and Quantum Mechanics. Journal of Philosophical Logic 30 (2):97-119.
    The paper consists of two parts. The first part begins with the problem of whether the original three-valued calculus, invented by J. Łukasiewicz, really conforms to his philosophical and semantic intuitions. I claim that one of the basic semantic assumptions underlying Łukasiewicz's three-valued logic should be that if under any possible circumstances a sentence of the form "X will be the case at time t" is true (resp. false) at time t, then this sentence must be already true (resp. false) (...)
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  33. Niels Bohr (1986). Do Quanta Need a New Logic? In Robert G. Colodny (ed.), From Quarks to Quasars: Philosophical Problems of Modern Physics. University of Pittsburgh Press. pp. 7--229.
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  34. Robert Bonnet & Matatyahu Rubin (2004). On Poset Boolean Algebras of Scattered Posets with Finite Width. Archive for Mathematical Logic 43 (4):467-476.
    We prove that the poset algebra of every scattered poset with finite width is embeddable in the poset algebra of a well ordered poset.
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  35. William Boos (1996). Mathematical Quantum Theory I: Random Ultrafilters as Hidden Variables. Synthese 107 (1):83 - 143.
    The basic purpose of this essay, the first of an intended pair, is to interpret standard von Neumann quantum theory in a framework of iterated measure algebraic truth for mathematical (and thus mathematical-physical) assertions — a framework, that is, in which the truth-values for such assertions are elements of iterated boolean measure-algebras (cf. Sections 2.2.9, 5.2.1–5.2.6 and 5.3 below).The essay itself employs constructions of Takeuti's boolean-valued analysis (whose origins lay in work of Scott, Solovay, Krauss and others) to provide a (...)
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  36. Alfons Borgers (1958). Bohr Niels. The Causality Problem in Atomic Physics. New Theories in Physics, Conference Organized in Collaboration with The International Union of Physics and The Polish Intellectual Co-Operation Committee, Warsaw, May 30th-June 3rd 1938, International Institute of Intellectual Co-Operation, Paris 1939, Pp. 11–38. Discussion, Pp. 38–45, by C. Białobrzeski, L. Brillouin, Jean-Louis Destouches, J. Von Neumann, and the Author.Heisenberg Werner. Language and Reality in Modern Physics. Physics and Philosophy, The Revolution in Modern Science, by Heisenberg Werner, Harper & Brothers, New York 1958, Pp. 167–186.Beth Evert Willem. Die Stellung der Logik Im Gebäude der Heutigen Wissenschaft. Studium Generate, Vol. 8 , Pp. 425–431. [REVIEW] Journal of Symbolic Logic 23 (1):66.
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  37. J. Brabec & P. Pták (1982). On Compatibility in Quantum Logics. Foundations of Physics 12 (2):207-212.
    We offer a variant of the intrinsic definition of compatibility in logics. We shown that any compatible subset can be embedded into a Boolean σ-algebra, we show how the algebra is constructed, and we demonstrate that our definition cannot be weakened unless we put additional assumptions on the logic.
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  38. Miro Brada, Chess Composition as an Art.
    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.
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  39. Miro Brada, Paradox of Religion...
    Religion supposes another world after death: paradise / hell / nirvana / karma... We live in incomplete world, because there is other 'truer' world. This replicates Plato philosophy (428-347 BC): behind something, is something, is something - till the pure idea (final judgement, karma, etc). In contrast, 'I think, therefore I am' (Descartes, 1637), showed the reality independent of Plato's parallel worlds. When I am thinking, regardless of what, 'I am' - whether there is or not 'truer' world. I show (...)
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  40. Ross T. Brady & Andrea Meinander (2013). Distribution in the Logic of Meaning Containment and in Quantum Mechanics. In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Springer. pp. 223--255.
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  41. Joseph E. Brenner (2010). The Philosophical Logic of Stéphane Lupasco (1900–1988). Logic and Logical Philosophy 19 (3):243-285.
    The advent of quantum mechanics in the early 20 th Century had profound consequences for science and mathematics, for philosophy (Schrödinger), and for logic (von Neumann). In 1968, Putnam wrote that quantum mechanics required a revolution in our understanding of logic per se. However, applications of quantum logics have been little explored outside the quantum domain. Dummett saw some implications of quantum logic for truth, but few philosophers applied similar intuitions to epistemology or ontology. Logic remained a truth-functional ’science’ of (...)
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  42. T. A. Brody (1984). On Quantum Logic. 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 logic, forms a subset of a slight (...)
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  43. Jan Broekaert, Diederik Aerts & Bart D’Hooghe (2006). The Generalised Liar Paradox: A Quantum Model and Interpretation. [REVIEW] Foundations of Science 11 (4):399-418.
    The formalism of abstracted quantum mechanics is applied in a model of the generalized Liar Paradox. Here, the Liar Paradox, a consistently testable configuration of logical truth properties, is considered a dynamic conceptual entity in the cognitive sphere (Aerts, Broekaert, & Smets, [Foundations of Science 1999, 4, 115–132; International Journal of Theoretical Physics, 2000, 38, 3231–3239]; Aerts and colleagues[Dialogue in Psychology, 1999, 10; Proceedings of Fundamental Approachs to Consciousness, Tokyo ’99; Mind in Interaction]. Basically, the intrinsic contextuality of the truth-value (...)
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  44. 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.
    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 logic of its experimental propositions (...)
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  45. Jeffrey Bub (1994). How to Interpret Quantum Mechanics. Erkenntnis 41 (2):253 - 273.
    I formulate the interpretation problem of quantum mechanics as the problem of identifying all possible maximal sublattices of quantum propositions that can be taken as simultaneously determinate, subject to certain constraints that allow the representation of quantum probabilities as measures over truth possibilities in the standard sense, and the representation of measurements in terms of the linear dynamics of the theory. The solution to this problem yields a modal interpretation that I show to be a generalized version of Bohm's hidden (...)
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  46. Jeffrey Bub (1994). On the Structure of Quantal Proposition Systems. Foundations of Physics 24 (9):1261-1279.
    I define sublaltices of quantum propositions that can be taken as having determinate (but perhaps unknown) truth values for a given quantum state, in the sense that sufficiently many two-valued maps satisfying a Boolean homomorphism condition exist on each determinate sublattice to generate a Kolmogorov probability space for the probabilities defined by the slate. I show that these sublattices are maximal, subject to certain constraints, from which it follows easily that they are unique. I discuss the relevance of this result (...)
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  47. Jeffrey Bub (1982). Quantum Logic, Conditional Probability, and Interference. 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 plays a (...)
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  48. Jeffrey Bub (1981). Hidden Variables and Quantum Logic — a Sceptical Review. Erkenntnis 16 (2):275 - 293.
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  49. Jeffrey Bub (1980). Book Review:Quantum Logic Peter Mittelstaedt. [REVIEW] Philosophy of Science 47 (2):332-.
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  50. Jeffrey Bub (1979). Some Reflections on Quantum Logic and Schrödinger's Cat. British Journal for the Philosophy of Science 30 (1):27-39.
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