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  1. The Philosophy of Alternative Logics.Andrew Aberdein & Stephen Read - 2009 - 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. Relational Hidden Variables and Non-Locality.Samson Abramsky - 2013 - 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. Analogues of Quantum Complementarity in the Theory of Automata - a Prolegomenon to the Philosophy of Quantum Mechanics.T. Acton, S. Caffrey, S. Dunn, P. Vinson & K. Svozil - 1998 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 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. La mecánica cuántica y la conceptualidad: materia, historias, semántica y espacio-tiempo.Diederik Aerts - 2013 - Scientiae Studia 11 (1):75-99.
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  5. Why the Disjunction in Quantum Logic is Not Classical.Diederik Aerts, Ellie D'Hondt & Liane Gabora - 2000 - 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. Analysis of Quantum Probability Theory. II.James Aken - 1986 - Journal of Philosophical Logic 15 (3):333 - 367.
  7. Analysis of Quantum Probability Theory. I.James Aken - 1985 - Journal of Philosophical Logic 14 (3):267 - 296.
  8. Dragalin AG. Matématičéskij Intuicionizm. Vvédénié V Téoriú Dokazatél'stv. Russian Original of the Preceding. Matématičéskaá Logika I Osnovaniá Matématiki,“Nauka,” Moscow 1979, 256 Pp. Deutsch D.. Quantum Theory, the Church–Turing Principle and the Universal Quantum Computer. Proceedings of the Royal Society of London, Ser. A Vol. 400 (1985), Pp. 97–117. [REVIEW]Urquhart Alasdair - 1990 - Journal of Symbolic Logic 55 (3):1309-1310.
  9. Helmut Reich's Proposal.John R. Albright - 2003 - Zygon 38 (2):435-439.
    A form of logic called relational and contextual reasoning is put forward as an improvement over other, more familiar types of logic. Developmental ideas are used to show how maturity ordinarily leads people away from binary (true/false) logic to systems of reasoning that are more subtle and better suited to making decisions in the face of ambiguity.
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  10. Perhaps (?), New logical foundations are needed for quantum mechanics.J. Almog - 1978 - Logique Et Analyse 21 (82):251.
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  11. The Quantum Logic of Zeno: Misconceptions and Restorations.Constantin Antonopoulos - 2007 - Acta Philosophica 16 (2):265-284.
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  12. LK, LJ, Dual Intuitionistic Logic, and Quantum Logic.Hiroshi Aoyama - 2004 - 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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  13. 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]K. O. Apel - 1979 - International Logic Review 12 (19-24):156.
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  14. Does Science Influence the Logic We Ought to Use: A Reflection on the Quantum Logic Controversy.Michael Ashcroft - 2010 - 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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  15. Elasticity and Metastability Limit in Supercooled Liquids: A Lattice Model.A. Attanasi, A. Cavagna & J. Lorenzana - 2007 - Philosophical Magazine 87 (3-5):441-448.
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  16. Quantum Logic.Iep Author - 2016
    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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  17. Is Logic Empirical?Guido Bacciagaluppi - unknown
    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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  18. Robert Rosen's Work and Complex Systems Biology.I. C. Baianu - 2006 - 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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  19. Complex Non-Linear Biodynamics in Categories, Higher Dimensional Algebra and ŁUkasiewicz''“Moisil Topos: Transformations of Neuronal, Genetic and Neoplastic Networks.I. C. Baianu, R. Brown, G. Georgescu & J. F. Glazebrook - 2006 - Axiomathes 16 (1):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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  20. A Dynamic-Logical Perspective on Quantum Behavior.A. Baltag & S. Smets - 2008 - 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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  21. Logics of Informational Interactions.Alexandru Baltag & Sonja Smets - forthcoming - 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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  22. 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, 1969), Pirón (Foundations of Quantum Physics, (...)
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  23. 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 theories, with (...)
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  24. The Logic of Quantum Programs.Alexandru Baltag & Sonja Smets - unknown
    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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  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 such theory naturally (...)
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  26. Review: Peter Fireman, Perceptualistic Theory of Knowledge. [REVIEW]Charles A. Baylis - 1960 - Journal of Symbolic Logic 25 (1):76-76.
  27. 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 put forward a simple and natural semantical framework (...)
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  28. Orthospaces and Quantum Logic.J. L. Bell - 1985 - 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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  29. Elementary Propositions and Independence.John L. Bell & William Demopoulos - 1996 - Notre Dame Journal of Formal Logic 37 (1):112-124.
    This paper is concerned with Wittgenstein's early doctrine of the independence of elementary propositions. Using the notion of a free generator for a logical calculus–a concept we claim was anticipated by Wittgenstein–we show precisely why certain difficulties associated with his doctrine cannot be overcome. We then show that Russell's version of logical atomism–with independent particulars instead of elementary propositions–avoids the same difficulties.
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  30. 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, negation crucially does not. (...)
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  31. On State Transformations Induced by Yes-No Experiments, in the Context of Quantum Logic.E. G. Beltrametti & G. Cassinelli - 1977 - Journal of Philosophical Logic 6 (1):369 - 379.
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  32. Quantum Mechanics Andp-Adic Numbers.E. G. Beltrametti & G. Cassinelli - 1972 - 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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  33. Current Issues in Quantum Logic.Enrico G. Beltrametti & Bas C. Van Fraassen - 1981
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  34. A Formal Construction of the Spacetime Manifold.Thomas Benda - 2008 - Journal of Philosophical Logic 37 (5):441 - 478.
    The spacetime manifold, the stage on which physics is played, is constructed ab initio in a formal program that resembles the logicist reconstruction of mathematics. Zermelo’s set theory extended by urelemente serves as a framework, to which physically interpretable proper axioms are added. From this basis, a topology and subsequently a Hausdorff manifold are readily constructed which bear the properties of the known spacetime manifold. The present approach takes worldlines rather than spacetime points to be primitive, having them represented by (...)
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  35. Review: R. Vaidyanathaswamy, On the Group-Operations of a Boolean Algebra. [REVIEW]Albert A. Bennett - 1937 - Journal of Symbolic Logic 2 (3):142-142.
  36. Three Identities for Ortholattices.Ladislav Beran - 1976 - Notre Dame Journal of Formal Logic 17 (2):251-252.
  37. Duality for the Logic of Quantum Actions.Jort M. Bergfeld, Kohei Kishida, Joshua Sack & Shengyang Zhong - 2015 - Studia Logica 103 (4):781-805.
    In this paper we show a duality between two approaches to represent quantum structures abstractly and to model the logic and dynamics therein. One approach puts forward a “quantum dynamic frame” :2267–2282, 2005), a labelled transition system whose transition relations are intended to represent projections and unitaries on a Hilbert space. The other approach considers a “Piron lattice”, which characterizes the algebra of closed linear subspaces of a Hilbert space. We define categories of these two sorts of structures and show (...)
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  38. Review: Hans Reichenbach, Elements of Symbolic Logic. [REVIEW]George D. W. Berry - 1949 - Journal of Symbolic Logic 14 (1):50-52.
  39. Review: Hans Reichenbach, Henri Savonnet, Introduction a la Logistique. [REVIEW]George D. W. Berry - 1947 - Journal of Symbolic Logic 12 (3):86-87.
  40. Review: M. Strauss, Formal Problems of Probability Theory in the Light of Quantum Mechanics. [REVIEW]Evert Beth - 1940 - Journal of Symbolic Logic 5 (2):72-73.
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  41. 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]Evert Beth - 1940 - Journal of Symbolic Logic 5 (2):72-73.
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  42. What the Liar Paradox Can Reveal About the Structure of Our Minds.Erhard Bieberich - manuscript
    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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  43. Three-Valued Logic, Indeterminacy and Quantum Mechanics.Tomasz Bigaj - 2001 - 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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  44. Lattice Theory.Garrett Birkhoff - 1940 - Journal of Symbolic Logic 5 (4):155-157.
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  45. The Logic of Quantum Mechanics.Garrett Birkhoff & John von Neumann - 1937 - Journal of Symbolic Logic 2 (1):44-45.
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  46. Do Quanta Need a New Logic?Niels Bohr - 1986 - 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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  47. On Poset Boolean Algebras of Scattered Posets with Finite Width.Robert Bonnet & Matatyahu Rubin - 2003 - 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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  48. Mathematical Quantum Theory I: Random Ultrafilters as Hidden Variables.William Boos - 1996 - 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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  49. Review: Patrick Suppes, Axiomatic Set Theory. [REVIEW]Alfons Borgers - 1960 - Journal of Symbolic Logic 25 (3):277-278.
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  50. Review: Niels Bohr, The Causality Problem in Atomic Physics; Werner Heisenberg, Language and Reality in Modern Physics; Evert Willem Beth, Die Stellung der Logik Im Gebaude der Heutigen Wissenschaft. [REVIEW]Alfons Borgers - 1958 - Journal of Symbolic Logic 23 (1):66-66.
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