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  1. Bob Coecke, Edward Grefenstette & Mehrnoosh Sadrzadeh (2013). Lambek Vs. Lambek: Functorial Vector Space Semantics and String Diagrams for Lambek Calculus. Annals of Pure and Applied Logic 164 (11):1079-1100.
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  2. Bob Coecke & Raymond Lal (2013). Causal Categories: Relativistically Interacting Processes. [REVIEW] 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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  3. Bob Coecke, Prakash Panangaden & Peter Selinger (2012). Preface. Foundations of Physics 42 (7):817-818.
  4. Bob Coecke & Robert W. Spekkens (2012). Picturing Classical and Quantum Bayesian Inference. 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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  5. Alexander Razborov, Bob Coecke, Zoé Chatzidakis, Bjørn Kjos, Nicolaas P. Landsman, Lawrence S. Moss, Dilip Raghavan, Tom Scanlon, Ernest Schimmerling & Henry Towsner (2011). 2010 North American Annual Meeting of the Association for Symbolic Logic. Bulletin of Symbolic Logic 17 (1).
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  6. Bob Coecke, David J. Moore & Sonja Smets (2004). Logic of Dynamics and Dynamics of Logic: Some Paradigm Examples. In. In S. Rahman J. Symons (ed.), Logic, Epistemology, and the Unity of Science. Kluwer Academic Publisher. 527--555.
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  7. Bob Coecke (2002). Disjunctive Quantum Logic in Dynamic Perspective. 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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  8. Bob Coecke (2002). Quantum Logic in Intuitionistic Perspective. 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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  9. Diederik Aerts & Bob Coecke (1999). The Creation-Discovery-View: Towards a Possible Explanation of Quantum Reality. In. In Maria Luisa Dalla Chiara (ed.), Language, Quantum, Music. 105--116.
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  10. Diederik Aerts, Bob Coecke & Sonja Smets (1999). On the Origin of Probabilities in Quantum Mechanics: Creative and Contextual Aspects. In S. Smets J. P. Van Bendegem G. C. Cornelis (ed.), Metadebates on Science. Vub-Press and Kluwer. 291--302.
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  11. Guido Bacciagaluppi, Bob Coecke & Isar Stubbe (1999). List of Contents: Volume 12, Number 1, February 1999. Foundations of Physics 29 (5).
  12. Karin Verelst & Bob Coecke (1999). Early Greek Thought and Perspectives for the Interpretation of Quantum Mechanics: Preliminaries to an Ontological Approach. In S. Smets J. P. Van Bendegem G. C. Cornelis (ed.), Metadebates on Science. VUB-Press and 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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  13. Bob Coecke (1998). A Representation for Compound Quantum Systems as Individual Entities: Hard Acts of Creation and Hidden Correlations. [REVIEW] 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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  14. Bob Coecke (1998). A Representation for a Spin-S Entity as a Compound System in R3Consisting of 2S Individual Spin-1/2 Entities. 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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  15. Bob Coecke (1995). A Hidden Measurement Representation for Quantum Entities Described by Finite-Dimensional Complex Hilbert Spaces. 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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