18 found
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  1. 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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  2. 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.). 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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  3.  22
    Lambek Vs. Lambek: Functorial Vector Space Semantics and String Diagrams for Lambek Calculus.Bob Coecke, Edward Grefenstette & Mehrnoosh Sadrzadeh - 2013 - Annals of Pure and Applied Logic 164 (11):1079-1100.
    The Distributional Compositional Categorical model is a mathematical framework that provides compositional semantics for meanings of natural language sentences. It consists of a computational procedure for constructing meanings of sentences, given their grammatical structure in terms of compositional type-logic, and given the empirically derived meanings of their words. For the particular case that the meaning of words is modelled within a distributional vector space model, its experimental predictions, derived from real large scale data, have outperformed other empirically validated methods that (...)
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  4. List of Contents: Volume 12, Number 1, February 1999.Guido Bacciagaluppi, Bob Coecke & Isar Stubbe - 1999 - Foundations of Physics 29 (5).
  5.  10
    Logic of Dynamics and Dynamics of Logic: Some Paradigm Examples.Bob Coecke, David J. Moore & Sonja Smets - 2004 - In S. Rahman J. Symons (ed.), Logic, Epistemology, and the Unity of Science. Kluwer Academic Publisher. pp. 527--555.
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  6. On the Origin of Probabilities in Quantum Mechanics: Creative and Contextual Aspects.Diederik Aerts, Bob Coecke & Sonja Smets - 1999 - In S. Smets J. P. Van Bendegem G. C. Cornelis (ed.), Metadebates on Science. Vub-Press & Kluwer. pp. 291--302.
  7.  22
    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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  8.  29
    A Hidden Measurement Representation for Quantum Entities Described by Finite-Dimensional Complex Hilbert Spaces.Bob Coecke - 1995 - Foundations of Physics 25 (8):1185-1208.
    It will be shown that the probability calculus of a quantum mechanical entity can be obtained in a deterministic framework, embedded in a real space, by introducing a lack of knowledge in the measurements on that entity. For all n ∃ ℕ we propose an explicit model in $\mathbb{R}^{n^2 } $ , which entails a representation for a quantum entity described by an n-dimensional complex Hilbert space þn, namely, the “þn,Euclidean hidden measurement representation.” This Euclidean hidden measurement representation is also (...)
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  9.  55
    Picturing Classical and Quantum Bayesian Inference.Bob Coecke & Robert W. Spekkens - 2012 - Synthese 186 (3):651 - 696.
    We introduce a graphical framework for Bayesian inference that is sufficiently general to accommodate not just the standard case but also recent proposals for a theory of quantum Bayesian inference wherein one considers density operators rather than probability distributions as representative of degrees of belief. The diagrammatic framework is stated in the graphical language of symmetric monoidal categories and of compact structures and Frobenius structures therein, in which Bayesian inversion boils down to transposition with respect to an appropriate compact structure. (...)
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  10.  36
    The Creation-Discovery-View: Towards a Possible Explanation of Quantum Reality.Diederik Aerts & Bob Coecke - 1999 - In Maria Luisa Dalla Chiara, Roberto Giuntini & Federico Laudisa (eds.), Language, Quantum, Music. Springer. pp. 105--116.
    The creation discovery view and together with it its technically underlying hidden measurement formalism has been elaborated from the early eighties on, and many aspects of it have been exposed in different places [6, 7, 12, 13, 15, 16, 19, 20, 22, 23, 30–37]. In this paper we give an overview of the most important of these aspects.
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  11.  64
    A Representation for a Spin-S Entity as a Compound System in R3Consisting of 2S Individual Spin-1/2 Entities.Bob Coecke - 1998 - Foundations of Physics 28 (8):1347-1365.
    We generalize the results of Ref. 7 for the coherent states of a spin-1 entity to spin-S entities with S > 1 and to noncoherent spin states: through the introduction of “hidden correlations” (see Ref. 8) we introduce a representation for a spin-S entity as a compound system consisting of 2S “individual” spin-1/2 entities, each of them represented by a “proper state,” and such that we are able to consider a measurement on the spin-S entity as a measurement on each (...)
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  12.  68
    Causal Categories: Relativistically Interacting Processes. [REVIEW]Bob Coecke & Raymond Lal - 2013 - Foundations of Physics 43 (4):458-501.
    A symmetric monoidal category naturally arises as the mathematical structure that organizes physical systems, processes, and composition thereof, both sequentially and in parallel. This structure admits a purely graphical calculus. This paper is concerned with the encoding of a fixed causal structure within a symmetric monoidal category: causal dependencies will correspond to topological connectedness in the graphical language. We show that correlations, either classical or quantum, force terminality of the tensor unit. We also show that well-definedness of the concept of (...)
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  13.  43
    Disjunctive Quantum Logic in Dynamic Perspective.Bob Coecke - 2002 - Studia Logica 71 (1):47 - 56.
    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 properties of physical systems. This (...)
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  14.  6
    Disjunctive Quantum Logic in Dynamic Perspective.Bob Coecke - 2002 - Studia Logica 71 (1):47-56.
    In Coecke 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 properties of physical systems. This paper (...)
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  15.  17
    A Diagrammatic Derivation of the Hermitian Adjoint.John H. Selby & Bob Coecke - 2017 - Foundations of Physics 47 (9):1191-1207.
    We show that the physical principle, “the adjoint associates to each state a ‘test’ for that state”, fully characterises the Hermitian adjoint for pure quantum theory, therefore providing the adjoint with operational meaning beyond its standard mathematical definition. Moreover, we demonstrate that for general process theories, which all admit a diagrammatic representation, this physical principle induces a diagrammatic reflection operation.
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  16.  36
    Preface.Bob Coecke, Prakash Panangaden & Peter Selinger - 2012 - Foundations of Physics 42 (7):817-818.
  17.  6
    2010 North American Annual Meeting of the Association for Symbolic Logic.Alexander Razborov, Bob Coecke, Zoé Chatzidakis, Bjørn Kjos, Nicolaas P. Landsman, Lawrence S. Moss, Dilip Raghavan, Tom Scanlon, Ernest Schimmerling & Henry Towsner - 2011 - Bulletin of Symbolic Logic 17 (1):127-154.
  18. Interacting Conceptual Spaces I: Grammatical Composition of Concepts.Robin Piedeleu, Dan Marsden, Martha Lewis, Fabrizio Genovese, Bob Coecke & Joe Bolt - 2019 - In Peter Gärdenfors, Antti Hautamäki, Frank Zenker & Mauri Kaipainen (eds.), Conceptual Spaces: Elaborations and Applications. Springer Verlag.
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