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  1. added 2020-05-08
    Pan demos Alla ricerca di un nuovo pensiero.Donato Santarcangelo - 2020 - Dialoghi Mediterranei.
  2. added 2020-03-10
    The Quantum Logic of Direct-Sum Decompositions: The Dual to the Quantum Logic of Subspaces.David Ellerman - 2018 - Logic Journal of the IGPL 26 (1):1-13.
    ince the pioneering work of Birkhoff and von Neumann, quantum logic has been interpreted as the logic of subspaces of a Hilbert space. There is a progression from the usual Boolean logic of subsets to the "quantum logic" of subspaces of a general vector space--which is then specialized to the closed subspaces of a Hilbert space. But there is a "dual" progression. The set notion of a partition is dual to the notion of a subset. Hence the Boolean logic of (...)
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  3. added 2020-03-07
    Categoricity and Possibility. A Note on Williamson's Modal Monism.Iulian D. Toader - forthcoming - In Martin Blicha & Igor Sedlár (eds.), The Logica Yearbook 2019. London: College Publications. pp. 1-11.
    The paper sketches an argument against modal monism, more specifically against the reduction of physical possibility to metaphysical possibility. The argument is based on the non-categoricity of quantum logic.
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  4. added 2020-02-11
    Particles and Paradoxes: The Limits of Quantum Logic. Peter Gibbins.Allen Stairs - 1989 - Philosophy of Science 56 (4):712-714.
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  5. added 2020-02-11
    Studies in the Foundations of Quantum Mechanics.Allen Stairs - 1982 - Philosophy of Science 49 (3):481-484.
  6. added 2020-02-11
    The Logico-Algebraic Approach to Quantum Mechanics. Volume II: Contemporary Consolidation.James H. McGrath - 1980 - Philosophy of Science 47 (4):660-662.
  7. added 2020-02-11
    Book Review:The Logico-Algebraic Approach to Quantum Mechanics. Volume I: Historical Evolution C. A. Hooker.James H. McGrath - 1978 - Philosophy of Science 45 (1):145-148.
  8. added 2019-06-07
    Neumann on Eustathios. [REVIEW]Walter Leaf - 1894 - The Classical Review 8 (3):110-111.
  9. added 2019-06-06
    The Problem of Identity and a Justification for a Non-Reflexive Quantum Mechanics.D. Krause - 2014 - Logic Journal of the IGPL 22 (2):186-205.
    In this paper we try to justify our way of looking for an alternative approach to quantum mechanics, which is based on a non-classical logic. We consider two specific questions related to quantum theory, namely, entanglement and the indiscernibility of quanta. We characterize individuals, and then explain in what sense entanglement is a concept which can be applied to individuals in a restricted sense only. Then, we turn to indiscernibility and, after realizing that this concept is of a fundamental importance, (...)
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  10. added 2019-06-06
    The Quasi-Lattice of Indiscernible Elements.Mauri Cunha do Nascimento, Décio Krause & Hércules Araújo Feitosa - 2011 - Studia Logica 97 (1):101-126.
    The literature on quantum logic emphasizes that the algebraic structures involved with orthodox quantum mechanics are non distributive. In this paper we develop a particular algebraic structure, the quasi-lattice (J-lattice), which can be modeled by an algebraic structure built in quasi-set theory Q. This structure is non distributive and involve indiscernible elements. Thus we show that in taking into account indiscernibility as a primitive concept, the quasi-lattice that 'naturally' arises is non distributive.
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  11. added 2019-06-06
    Robert Rosen’s Work and Complex Systems Biology.I. C. Baianu - 2006 - Axiomathes 16 (1):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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  12. added 2019-06-06
    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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  13. added 2019-06-06
    Distribution, superposition and quantum logic.Jonathan Harrison - 1985 - Analysis 45 (4):204.
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  14. added 2019-06-06
    Hermann Dishkant. The First Order Predicate Calculus Based on the Logic of Quantum Mechanics. Reports on Mathematical Logic, No. 3 , Pp. 9–17. - G. N. Georgacarakos. Orthomodularity and Relevance. Journal of Philosophical Logic, Vol. 8 , Pp. 415–432. - G. N. Georgacarakos. Equationally Definable Implication Algebras for Orthomodular Lattices. Studia Logica, Vol. 39 , Pp. 5–18. - R. J. Greechie and S. P. Gudder. Is a Quantum Logic a Logic?Helvetica Physica Acta, Vol. 44 , Pp. 238–240. - Gary M. Hardegree. The Conditional in Abstract and Concrete Quantum Logic. The Logico-Algehraic Approach to Quantum Mechanics, Volume II, Contemporary Consolidation, Edited by C. A. Hooker, The University of Western Ontario Series in Philosophy of Science, Vol. 5, D. Reidel Publishing Company, Dordrecht, Boston, and London, 1979, Pp. 49–108. - Gary M. Hardegree. Material Implication in Orthomodular Lattices. Notre Dame Journal of Formal Logic, Vol. 22 , Pp. 163–182. - J. M. Jauch and C. Piron. What is “Q. [REVIEW]Alasdair Urquhart - 1983 - Journal of Symbolic Logic 48 (1):206-208.
  15. added 2019-06-06
    Sachs David. The Lattice of Subalgebras of a Boolean Algebra. Canadian Journal of Mathematics, Vol. 14 , Pp. 451–460.G. Gratzer - 1972 - Journal of Symbolic Logic 37 (1):190-191.
  16. added 2019-06-06
    Elements of Symbolic Logic.J. van Heijenoort - 1966 - Journal of Symbolic Logic 31 (4):675.
  17. added 2019-06-06
    Banaschewski B.. Hüllensysteme und Erweiterung von Quasi-Ordnungen. Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 2 , pp. 117–130. [REVIEW]J. R. Shoenfield - 1962 - Journal of Symbolic Logic 27 (2):235-236.
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  18. added 2019-06-06
    Lattice Structure of Space-Time.I. J. Good - 1958 - British Journal for the Philosophy of Science 9 (33):317.
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  19. added 2019-06-06
    Serrell Robert. Elements of Boolean Algebra for the Study of Information-Handling Systems. Proceedings of the I.R.E., Vol. 41 , Pp. 1366–1380.Serrell Robert. Correction. Proceedings of the I.R.E., Vol. 42 , P. 475. [REVIEW]Alonzo Church - 1954 - Journal of Symbolic Logic 19 (2):142-142.
  20. added 2019-06-06
    Vaidyanathaswamy R.. On the Group-Operations of a Boolean Algebra. The Journal of the Indian Mathematical Society, N.S. Vol. 2 , Pp. 250–254. [REVIEW]Albert A. Bennett - 1937 - Journal of Symbolic Logic 2 (3):142-142.
  21. added 2019-06-05
    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 cognitive science of (...)
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  22. added 2019-06-05
    Quantum Probability--Quantum Logic. Itamar Pitowsky.David Malament - 1992 - Philosophy of Science 59 (2):300-320.
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  23. added 2019-06-05
    Modern Logic and Quantum Mechanics. Rachel Wallace Garden.Richard Healey - 1985 - Philosophy of Science 52 (4):642-644.
  24. added 2019-06-05
    Quantum Logic. Peter Mittelstaedt.Jeffrey Bub - 1980 - Philosophy of Science 47 (2):332-335.
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  25. added 2019-06-05
    The Logical Analysis of Quantum Mechanics. Erhard Scheibe, J. B. Sykes.Edward MacKinnon - 1975 - Philosophy of Science 42 (1):96-100.
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  26. added 2019-05-24
    Simon Kochen and E. P. Specker. Logical Structures Arising in Quantum Theory. A Reprint of XL 507. The Logieo-Algebraic Approach to Quantum Mechanics, Volume I, Historicale Evolution, Edited by C. A. Hooker, The University of Western Ontario Series in Philosophy of Science, Vol. 5, D. Reidel Publishing Company, Dordrecht and Boston1975, Pp. 263–276. - Simon Kochen and E. P. Specker. The Calculus of Partial Propositional Functions. A Reprint of XL 508. The Logieo-Algebraic Approach to Quantum Mechanics, Volume I, Historical Evolution, Edited by C. A. Hooker, The University of Western Ontario Series in Philosophy of Science, Vol. 5, D. Reidel Publishing Company, Dordrecht and Boston1975, Pp. 277–292. - P.D. Finch. On the Structure of Quantum Logic. The Logieo-Algebraic Approach to Quantum Mechanics, Volume I, Historical Evolution, Edited by C. A. Hooker, The University of Western Ontario Series in Philosophy of Science, Vol. 5, D. Reidel Publishing Company, Dordrecht and Boston1975, Pp. [REVIEW]R. I. G. Hughes - 1985 - Journal of Symbolic Logic 50 (2):558-566.
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  27. added 2019-05-21
    Peter Gibbins. Particles and Paradoxes. The Limits of Quantum Logic. Cambridge University Press, Cambridge Etc. 1987, Xi + 181 Pp. [REVIEW]Maria Luisa Dalla Chiara - 1990 - Journal of Symbolic Logic 55 (1):354-355.
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  28. added 2019-05-21
    A. G. Dragalin. Matématičéskij Intuicionizm. Vvédénié V Téoriú Dokazatél'stv. Russian Original of the Preceding. Matématičéskaá Logika I Osnovaniá Matématiki, “Nauka,”Moscow1979, 256 Pp. - D. Deutsch. Quantum Theory, the Church–Turing Principle and the Universal Quantum Computer. Proceedings of the Royal Society of London, Ser. A Vol. 400 , Pp. 97–117. [REVIEW]Urquhart Alasdair - 1990 - Journal of Symbolic Logic 55 (3):1309-1310.
  29. added 2019-01-28
    On the Notion of Truth in Quantum Mechanics: A Category-Theoretic Standpoint.Vassilios Karakostas & Elias Zafiris - 2016 - In Diederik Aerts, Christian de Ronde, Hector Freytes & Roberto Giuntini (eds.), Probing the Meaning and Structure of Quantum Mechanics: Semantics, Dynamics and Identity. World Scientific. pp. 1-43.
    The category-theoretic representation of quantum event structures provides a canonical setting for confronting the fundamental problem of truth valua- tion in quantum mechanics as exemplified, in particular, by Kochen-Specker’s theorem. In the present study, this is realized on the basis of the existence of a categorical adjunction between the category of sheaves of variable local Boolean frames, constituting a topos, and the category of quantum event al- gebras. We show explicitly that the latter category is equipped with an object of (...)
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  30. added 2019-01-28
    Boolean Information Sieves: A Local-to-Global Approach to Quantum Information.Elias Zafiris - 2010 - International Journal of General Systems 39 (8):873-895.
    We propose a sheaf-theoretic framework for the representation of a quantum observable structure in terms of Boolean information sieves. The algebraic representation of a quantum observable structure in the relational local terms of sheaf theory effectuates a semantic transition from the axiomatic set-theoretic context of orthocomplemented partially ordered sets, la Birkhoff and Von Neumann, to the categorical topos-theoretic context of Boolean information sieves, la Grothendieck. The representation schema is based on the existence of a categorical adjunction, which is used as (...)
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  31. added 2019-01-28
    Quantum Observables Algebras and Abstract Differential Geometry: The Topos-Theoretic Dynamics of Diagrams of Commutative Algebraic Localizations.Elias Zafiris - 2007 - International Journal of Theoretical Physics 46 (2):319-382.
    We construct a sheaf-theoretic representation of quantum observables algebras over a base category equipped with a Grothendieck topology, consisting of epimorphic families of commutative observables algebras, playing the role of local arithmetics in measurement situations. This construction makes possible the adaptation of the methodology of Abstract Differential Geometry (ADG), à la Mallios, in a topos-theoretic environment, and hence, the extension of the “mechanism of differentials” in the quantum regime. The process of gluing information, within diagrams of commutative algebraic localizations, generates (...)
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  32. added 2019-01-28
    Category-Theoretic Analysis of the Notion of Complementarity for Quantum Systems.Elias Zafiris - 2006 - International Journal of General Systems 35 (1):69-89.
    In this paper we adopt a category-theoretic viewpoint in order to analyze the semantics of complementarity for quantum systems. Based on the existence of a pair of adjoint functors between the topos of presheaves of the Boolean kind of structure and the category of the quantum kind of structure, we establish a twofold complementarity scheme which constitutes an instance of the concept of adjunction. It is further argued that the established scheme is inextricably connected with a realistic philosophical attitude, although (...)
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  33. added 2019-01-28
    Generalized Topological Covering Systems on Quantum Events' Structures.Elias Zafiris - 2006 - Journal of Physics A: Mathematics and Applications 39 (6):1485-1505.
    Homologous operational localization processes are effectuated in terms of generalized topological covering systems on structures of physical events. We study localization systems of quantum events' structures by means of Gtothendieck topologies on the base category of Boolean events' algebras. We show that a quantum events algebra is represented by means of a Grothendieck sheaf-theoretic fibred structure, with respect to the global partial order of quantum events' fibres over the base category of local Boolean frames.
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  34. added 2019-01-28
    Sheaf-Theoretic Representation of Quantum Measure Algebras.Elias Zafiris - 2006 - Journal of Mathematical Physics 47 (9).
    We construct a sheaf-theoretic representation of quantum probabilistic structures, in terms of covering systems of Boolean measure algebras. These systems coordinatize quantum states by means of Boolean coefficients, interpreted as Boolean localization measures. The representation is based on the existence of a pair of adjoint functors between the category of presheaves of Boolean measure algebras and the category of quantum measure algebras. The sheaf-theoretic semantic transition of quantum structures shifts their physical significance from the orthoposet axiomatization at the level of (...)
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  35. added 2019-01-28
    On Quantum Event Structures. III. Object of Truth Values.Elias Zafiris - 2004 - Foundations Of Physics Letters 17 (5):403-432.
    In this work we expand the foundational perspective of category theory on quantum event structures by showing the existence of an object of truth values in the category of quantum event algebras, characterized as subobject classifier. This object plays the corresponking role that the two-valued Boolean truth values object plays in a classical event structure. We construct the object of quantum truth values explicitly and argue that it constitutes the appropriate choice for the valuation of propositions describing the behavior of (...)
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  36. added 2019-01-28
    Interpreting Observables in a Quantum World From the Categorial Standpoint.Elias Zafiris - 2004 - International Journal of Theoretical Physics 43 (1):265-298.
    We develop a relativistic perspective on structures of quantum observables, in terms of localization systems of Boolean coordinatizing charts. This perspective implies that the quantum world is comprehended via Boolean reference frames for measurement of observables, pasted together along their overlaps. The scheme is formalized categorically, as an instance of the adjunction concept. The latter is used as a framework for the specification of a categorical equivalence signifying an invariance in the translational code of communication between Boolean localizing contexts and (...)
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  37. added 2019-01-27
    Loops, Projective Invariants, and the Realization of the Borromean Topological Link in Quantum Mechanics.Elias Zafiris - 2016 - Quantum Studies: Mathematics and Foundations 3 (4):337-359.
    All the typical global quantum mechanical observables are complex relative phases obtained by interference phenomena. They are described by means of some global geometric phase factor, which is thought of as the “memory” of a quantum system undergoing a “cyclic evolution” after coming back to its original physical state. The origin of a geometric phase factor can be traced to the local phase invariance of the transition probability assignment in quantum mechanics. Beyond this invariance, transition probabilities also remain invariant under (...)
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  38. added 2019-01-27
    Boolean Localization Of Quantum Events: A Processual Sheaf-Theoretic Approach.Elias Zafiris - 2016 - In David Ray Griffin, Michael Epperson & Timothy E. Eastman (eds.), Physics and Speculative Philosophy: Potentiality in Modern Science. De Gruyter. pp. 107-126.
  39. added 2019-01-27
    Foundations of Relational Realism: A Topological Approach to Quantum Mechanics and the Philosophy of Nature.Michael Epperson & Elias Zafiris - 2013 - Lexington Books.
    Foundations of Relational Realism presents an intuitive interpretation of quantum mechanics, based on a revised decoherent histories interpretation, structured within a category theoretic topological formalism. -/- If there is a central conceptual framework that has reliably borne the weight of modern physics as it ascends into the twenty-first century, it is the framework of quantum mechanics. Because of its enduring stability in experimental application, physics has today reached heights that not only inspire wonder, but arguably exceed the limits of intuitive (...)
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  40. added 2018-07-11
    Teleportative Observers Versus Special Relativity Observers: The Logical Universal Chronology and Presentism.James Goetz - manuscript
    Various authors use the Rietdijk–Putnam argument while proposing that special relativity implies eternalism. For example, special relativity observers are limited by the relativity of simultaneity and cannot detect a preferred universal chronology. Any pair of special relativity observers that are causally disconnected to each other will detect ubiquitous relativistic reversals of chronology. The argument concludes that the reversals of chronology imply that all events in the past, present, and future exist "now." However, I introduce "teleportative observers" which cohere with wormhole (...)
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  41. added 2018-02-18
    John von Neumann's Mathematical “Utopia” in Quantum Theory.Giovanni Valente - 2008 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 39 (4):860-871.
    This paper surveys John von Neumann's work on the mathematical foundations of quantum theories in the light of Hilbert's Sixth Problem concerning the geometrical axiomatization of physics. We argue that in von Neumann's view geometry was so tied to logic that he ultimately developed a logical interpretation of quantum probabilities. That motivated his abandonment of Hilbert space in favor of von Neumann algebras, specifically the type II1II1 factors, as the proper limit of quantum mechanics in infinite dimensions. Finally, we present (...)
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  42. added 2018-02-17
    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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  43. added 2017-11-09
    In the Chaos of Today's Society: The Dynamics of Collapse as Another Shift in the Quantum Anthropology of Heidi Ann Russell.Radek Trnka - 2015 - Prague: Togga.
    The presented study introduces a new theoretical model of collapse for social, cultural, or political systems. Based on the current form of quantum anthropology conceptualized by Heidi Ann Russell, further development of this field is provided. The new theoretical model is called the spiral model of collapses, and is suggested to provide an analytical framework for collapses in social, cultural, and political systems. The main conclusions of this study are: 1) The individual crises in the period before a collapse of (...)
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  44. added 2017-02-14
    Modal-Type Orthomodular Logic.Trixie Wagner & Andreas Schouml - forthcoming - Mathematical Logic Quarterly.
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  45. added 2017-02-13
    Extremal Consequence Operations.D. W. Miller - 2000 - Bulletin of the Section of Logic 29 (3):99-107.
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  46. added 2017-02-12
    Would Leibniz Have Shared von Neumann's Logical Physicalism?Witold Marciszewski - 1995 - Logic and Logical Philosophy 3:115-128.
    This paper represents such an amateur approach; hence any comments backed up by professional erudition will be highly appreciated. Let me start from an attempt to sketch a relationship between professionals’ and amateurs’ contributions. The latter may be compared with the letters to the Editor of a journal, written by perceptive readers, while professionals contribute to the very content of the journal in question. Owing to such letters, the Editor and his professional staff can become more aware of the responses (...)
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  47. added 2017-02-11
    Independence in Operator Algebras.StanisŁaw Goldstein, Andrzej Łuczak & Ivan F. Wilde - 1999 - Foundations of Physics 29 (1):79-89.
    Various notions of independence of observables have been proposed within the algebraic framework of quantum field theory. We discuss relationships between these and the recently introduced notion of logical independence in a general operator-algebraic context. We show that C*-independence implies an analogue of classical independence.
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  48. added 2017-02-11
    Review: Luis E. Sanchis, Set Theory -- An Operational Approach. [REVIEW]J. P. Mayberry - 1998 - Journal of Symbolic Logic 63 (2):751-752.
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  49. added 2017-02-11
    Review: Zarko Mijajlovic, Zoran Markovic, Kosta Dosen, Hilbert's Problems and Logic. [REVIEW]Boban Velickovic - 1987 - Journal of Symbolic Logic 52 (4):1049-1050.
  50. added 2017-02-11
    Review: Kathleen Levitz, Hilbert Levitz, Logic and Boolean Algebra. [REVIEW]Diane Resek - 1981 - Journal of Symbolic Logic 46 (2):420-421.
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