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  1. Quantum Entanglement: An Analysis via the Orthogonality Relation.Shengyang Zhong - 2023 - Foundations of Physics 53 (4):1-49.
    In the literature there has been evidence that a kind of relational structure called a quantum Kripke frame captures the essential characteristics of the orthogonality relation between pure states of quantum systems, and thus is a good qualitative mathematical model of quantum systems. This paper adds another piece of evidence by providing a tensor-product construction of two finite-dimensional quantum Kripke frames. We prove that this construction is exactly the qualitative counterpart of the tensor-product construction of two finite-dimensional Hilbert spaces over (...)
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  • Philosophy of Quantum Probability - An empiricist study of its formalism and logic.Ronnie Hermens - unknown
    The use of probability theory is widespread in our daily life as well as in scientific theories. In virtually all cases, calculations can be carried out within the framework of classical probability theory. A special exception is given by quantum mechanics, which gives rise to a new probability theory: quantum probability theory. This dissertation deals with the question of how this formalism can be understood from a philosophical and physical perspective. The dissertation is divided into three parts. In the first (...)
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  • Basic ontology and the ontology of the phenomenological life world: A proposal.Wim Christiaens - 2006 - Foundations of Science 11 (3):249-274.
    The condition of explicit theoretically discursive cognitive performance, as it culminates in scientific activity, is, I claim, the life world. I contrast life world and scientific world and argue that the latter arises from the first and that contrary to the prevailing views the scientific world (actually, worlds, since the classical world is substantially different from the quantum world) finds its completion in the life world and not the other way around. In other words: the closure we used to search (...)
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  • Quantum logic in intuitionistic perspective.Bob Coecke - 2002 - Studia Logica 70 (3):411-440.
    In their seminal paper Birkhoff and von Neumann revealed the following dilemma:[ ] whereas for logicians the orthocomplementation properties of negation were the ones least able to withstand a critical analysis, the study of mechanics points to the distributive identities as the weakest link in the algebra of logic.
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  • 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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  • Early greek thought and perspectives for the interpretation of quantum mechanics: Preliminaries to an ontological approach.Karin Verelst & Bob Coecke - 1999 - In S. Smets J. P. Van Bendegem G. C. Cornelis (ed.), Metadebates on Science. VUB-Press & Kluwer.
    It will be shown in this article that an ontological approach for some problems related to the interpretation of Quantum Mechanics could emerge from a re-evaluation of the main paradox of early Greek thought: the paradox of Being and non-Being, and the solutions presented to it by Plato and Aristotle. More well known are the derivative paradoxes of Zeno: the paradox of motion and the paradox of the One and the Many. They stem from what was perceived by classical philosophy (...)
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  • In defense of operational quantum logic.Sonja Smets - 2002 - Logic and Logical Philosophy 11:191-212.
    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 conceptual machinery (...)
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  • The modes of physical properties in the logical foundations of physics.Sonja Smets - 2005 - Logic and Logical Philosophy 14 (1):37-53.
    We present a conceptual analysis of the notions of actual physical property and potential physical property as used by theoretical physicists/mathematicians working in the domain of operational quantum logic. We investigate how these notions are being used today and what role they play in the specified field of research. In order to do so, we will give a brief introduction to this area of research and explain it as a part of the discipline known as “mathematical metascience”. An in depth (...)
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  • (1 other version)Bohrification of operator algebras and quantum logic.Chris Heunen, Nicolaas P. Landsman & Bas Spitters - 2012 - Synthese 186 (3):719 - 752.
    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 be families (...)
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  • 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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  • Reasoning about Quantum Actions: A Logician's Perspective.Sonja Smets - 2013 - In Hanne Andersen, Dennis Dieks, Wenceslao J. Gonzalez, Thomas Uebel & Gregory Wheeler (eds.), New Challenges to Philosophy of Science. Springer Verlag. pp. 125--134.
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  • A Representation for Compound Quantum Systems as Individual Entities: Hard Acts of Creation and Hidden Correlations. [REVIEW]Bob Coecke - 1998 - Foundations of Physics 28 (7):1109-1135.
    We introduce an explicit definition for “hidden correlations” on individual entities in a compound system: when one individual entity is measured, this induces a well-defined transition of the “proper state” of the other individual entities. We prove that every compound quantum system described in the tensor product of a finite number of Hilbert spaces can be uniquely represented as a collection of individual entities between which there exist such hidden correlations. We investigate the significance of these hidden correlation representations within (...)
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  • Logic of Dynamics and Dynamics of Logic: Some Paradigm Examples.Bob Coecke, David J. Moore & Sonja Smets - 2004 - In S. Rahman (ed.), Logic, Epistemology, and the Unity of Science. Dordrecht: Kluwer Academic Publishers. pp. 527--555.
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  • Constructible models of orthomodular quantum logics.Piotr Wilczek - unknown
    We continue in this article the abstract algebraic treatment of quantum sentential logics Wil. The Notions borrowed from the field of Model Theory and Abstract Algebraic Logic - AAL (i.e., consequence relation, variety, logical matrix, deductive filter, reduced product, ultraproduct, ultrapower, Frege relation, Leibniz congruence, Suszko congruence, Leibniz operator) are applied to quantum logics. We also proved several equivalences between state property systems (Jauch-Piron-Aerts line of investigations) and AAL treatment of quantum logics (corollary 18 and 19). We show that there (...)
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