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  1. Diederik Aerts (2014). Quantum and Concept Combination, Entangled Measurements, and Prototype Theory. Topics in Cognitive Science 6 (1):129-137.
    We analyze the meaning of the violation of the marginal probability law for situations of correlation measurements where entanglement is identified. We show that for quantum theory applied to the cognitive realm such a violation does not lead to the type of problems commonly believed to occur in situations of quantum theory applied to the physical realm. We briefly situate our quantum approach for modeling concepts and their combinations with respect to the notions of “extension” and “intension” in theories of (...)
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  2. Diederik Aerts (2013). La mecánica cuántica y la conceptualidad: materia, historias, semántica y espacio-tiempo. Scientiae Studia 11 (1):75-99.
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  3. Diederik Aerts (2013). The Quantum Mechanics and Conceptuality: Matter, Histories, Semantics, and Space-Time. Scientiae Studia 11 (1):75-99.
    Elaboramos aquí una nueva interpretación propuesta recientemente de la teoría cuántica, según la cual las partículas cuánticas son consideradas como entidades conceptuales que median entre los pedazos de materia ordinaria los cuales son considerados como estructuras de memoria para ellos. Nuestro objetivo es identificar qué es lo equivalente para el ámbito cognitivo humano de lo que el espacio-tiempo físico es para el ámbito de las partículas cuánticas y de la materia ordinaria. Para ello, se identifica la noción de "historia" como (...)
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  4. Diederik Aerts, Jan Broekaert, Liane Gabora & Sandro Sozzo (2013). Quantum Structure and Human Thought. Behavioral and Brain Sciences 36 (3):274-276.
    We support the authors' claims, except that we point out that also quantum structure different from quantum probability abundantly plays a role in human cognition. We put forward several elements to illustrate our point, mentioning entanglement, contextuality, interference, and emergence as effects, and states, observables, complex numbers, and Fock space as specific mathematical structures.
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  5. Diederik Aerts, Liane Gabora & Sandro Sozzo (2013). Concepts and Their Dynamics: A Quantum‐Theoretic Modeling of Human Thought. Topics in Cognitive Science 5 (4):737-772.
    We analyze different aspects of our quantum modeling approach of human concepts and, more specifically, focus on the quantum effects of contextuality, interference, entanglement, and emergence, illustrating how each of them makes its appearance in specific situations of the dynamics of human concepts and their combinations. We point out the relation of our approach, which is based on an ontology of a concept as an entity in a state changing under influence of a context, with the main traditional concept theories, (...)
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  6. Diederik Aerts (2010). A Potentiality and Conceptuality Interpretation of Quantum Physics. Philosophica 83.
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  7. Diederik Aerts, Sonja Smets & Jean P. Van Bendegem (2010). The Contributions of Logic to the Foundations of Physics: Foreword. [REVIEW] Studia Logica 95 (1-2):1-3.
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  8. Diederik Aerts (2009). Quantum Particles as Conceptual Entities: A Possible Explanatory Framework for Quantum Theory. [REVIEW] Foundations of Science 14 (4):361-411.
    We put forward a possible new interpretation and explanatory framework for quantum theory. The basic hypothesis underlying this new framework is that quantum particles are conceptual entities. More concretely, we propose that quantum particles interact with ordinary matter, nuclei, atoms, molecules, macroscopic material entities, measuring apparatuses, in a similar way to how human concepts interact with memory structures, human minds or artificial memories. We analyze the most characteristic aspects of quantum theory, i.e. entanglement and non-locality, interference and superposition, identity and (...)
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  9. Liane Gabora & Diederik Aerts (2008). A Cross-Disciplinary Framework for the Description of Contextually Mediated Change. In World Scientific (ed.), Physics of Emergence and Organization. 109--134.
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  10. Diederik Aerts, Marek Czachor, Bart D.’Hooghe & Sandro Sozzo (2007). The Pet-Fish Problem on the World-Wide Web. Cognition 2008:2009.
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  11. Jan Broekaert, Diederik Aerts & Bart D.’Hooghe (2006). The Generalised Liar Paradox: A Quantum Model and Interpretation. [REVIEW] Foundations of Science 11 (4):399-418.
    The formalism of abstracted quantum mechanics is applied in a model of the generalized Liar Paradox. Here, the Liar Paradox, a consistently testable configuration of logical truth properties, is considered a dynamic conceptual entity in the cognitive sphere (Aerts, Broekaert, & Smets, [Foundations of Science 1999, 4, 115–132; International Journal of Theoretical Physics, 2000, 38, 3231–3239]; Aerts and colleagues[Dialogue in Psychology, 1999, 10; Proceedings of Fundamental Approachs to Consciousness, Tokyo ’99; Mind in Interaction]. Basically, the intrinsic contextuality of the truth-value (...)
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  12. Diederik Aerts & Liane Gabora (2005). A Theory of Concepts and Their Combinations I: The Structure of the Sets of Contexts and Properties. Aerts, Diederik and Gabora, Liane (2005) a Theory of Concepts and Their Combinations I.
    We propose a theory for modeling concepts that uses the state-context-property theory (SCOP), a generalization of the quantum formalism, whose basic notions are states, contexts and properties. This theory enables us to incorporate context into the mathematical structure used to describe a concept, and thereby model how context influences the typicality of a single exemplar and the applicability of a single property of a concept. We introduce the notion `state of a concept' to account for this contextual influence, and show (...)
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  13. Diederik Aerts & Liane Gabora (2005). A Theory of Concepts and Their Combinations II: A Hilbert Space Representation. .
    The sets of contexts and properties of a concept are embedded in the complex Hilbert space of quantum mechanics. States are unit vectors or density operators, and contexts and properties are orthogonal projections. The way calculations are done in Hilbert space makes it possible to model how context influences the state of a concept. Moreover, a solution to the combination of concepts is proposed. Using the tensor product, a procedure for describing combined concepts is elaborated, providing a natural solution to (...)
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  14. Liane Gabora & Diederik Aerts (2002). Contextualizing Concepts Using a Mathematical Generalization of the Quantum Formalism. .
    We outline the rationale and preliminary results of using the State Context Property (SCOP) formalism, originally developed as a generalization of quantum mechanics, to describe the contextual manner in which concepts are evoked, used, and combined to generate meaning. The quantum formalism was developed to cope with problems arising in the description of (1) the measurement process, and (2) the generation of new states with new properties when particles become entangled. Similar problems arising with concepts motivated the formal treatment introduced (...)
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  15. Diederik Aerts (2000). Editorial: Quantum, Mimesis and the Social Sciences. [REVIEW] Foundations of Science 5 (1):1-2.
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  16. Diederik Aerts, Sven Aerts, Jan Broekaert & Liane Gabora (2000). The Violation of Bell Inequalities in the Macroworld. Foundations of Physics 30 (9):1387-1414.
    We show that Bell inequalities can be violated in the macroscopic world. The macroworld violation is illustrated using an example involving connected vessels of water. We show that whether the violation of inequalities occurs in the microworld or the macroworld, it is the identification of nonidentical events that plays a crucial role. Specifically, we prove that if nonidentical events are consistently differentiated, Bell-type Pitowsky inequalities are no longer violated, even for Bohm's example of two entangled spin 1/2 quantum particles. We (...)
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  17. Diederik Aerts, Jan Broekaert & Liane Gabora, Intrinsic Contextuality as the Crux of Consciousness.
    A stream of conscious experience is extremely contextual; it is impacted by sensory stimuli, drives and emotions, and the web of associations that link, directly or indirectly, the subject of experience to other elements of the individual's worldview. The contextuality of one's conscious experience both enhances and constrains the contextuality of one's behavior. Since we cannot know first-hand the conscious experience of another, it is by way of behavioral contextuality that we make judgements about whether or not, and to what (...)
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  18. Diederik Aerts, Ellie D'Hondt & Liane Gabora (2000). Why the Disjunction in Quantum Logic is Not Classical. 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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  19. Diederik Aerts (1999). Editorial: Creativity and Science. [REVIEW] Foundations of Science 4 (2):111-112.
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  20. Diederik Aerts (ed.) (1999). Quantum Structures and the Nature of Reality: The Indigo Book of 'Einstein Meets Magritte'. Kluwer Academic.
    Quantum Structures and the Nature of Reality is a collection of papers written for an interdisciplinary audience about the quantum structure research within the International Quantum Structures Association. The advent of quantum mechanics has changed our scientific worldview in a fundamental way. Many popular and semi-popular books have been published about the paradoxical aspects of quantum mechanics. Usually, however, these reflections find their origin in the standard views on quantum mechanics, most of all the wave-particle duality picture. Contrary to relativity (...)
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  21. Diederik Aerts, Jan Broekaert & Liane Gabora (1999). Editorial: Formal and Informal Representations of Science. [REVIEW] Foundations of Science 4 (1):1-2.
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  22. Diederik Aerts, Jan Broekaert & Ernest Mathijs (eds.) (1999). Einstein Meets Magritte: An Interdisciplinary Reflection: The White Book of "Einstein Meets Magritte". Kluwer Academic.
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  23. Diederik Aerts, Jan Broekaert & Sonja Smets (1999). The Liar-Paradox in a Quantum Mechanical Perspective. Foundations of Science 4 (2):115-132.
    In this paper we concentrate on the nature of the liar paradox asa cognitive entity; a consistently testable configuration of properties. We elaborate further on a quantum mechanical model (Aerts, Broekaert and Smets, 1999) that has been proposed to analyze the dynamics involved, and we focus on the interpretation and concomitant philosophical picture. Some conclusions we draw from our model favor an effective realistic interpretation of cognitive reality.
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  24. 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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  25. 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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  26. Diederik Aerts (1998). Editorial: Synthesis and Analysis, Interdisciplinarity and Foundations. [REVIEW] Foundations of Science 3 (2):203-206.
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  27. Diederik Aerts (1998). The Entity and Modern Physics. In Elena Castellani (ed.), Interpreting Bodies. Princeton University Press. 223--257.
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  28. Diederik Aerts, Jan Broekaert & Sonja Smets (1998). Inconsistencies in Constituent Theories of World Views: Quantum Mechanical Examples. [REVIEW] Foundations of Science 3 (2):313-340.
    We put forward the hypothesis that there exist three basic attitudes towards inconsistencies within world views: (1) The inconsistency is tolerated temporarily and is viewed as an expression of a temporary lack of knowledge due to an incomplete or wrong theory. The resolution of the inconsistency is believed to be inherent to the improvement of the theory. This improvement ultimately resolves the contradiction and therefore we call this attitude the ‘regularising’ attitude; (2) The inconsistency is tolerated and both contradicting elements (...)
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  29. Diederik Aerts & Fritz Rohrlich (1998). Reduction. Foundations of Science 3 (1):27-35.
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  30. Diederik Aerts (1996). Relativity Theory: What is Reality? [REVIEW] Foundations of Physics 26 (12):1627-1644.
    In classical Newtonian physics there was a clear understanding of “what reality is.≓ Indeed in this classical view, reality at a certain time is the collection of all what is actual at this time, and this is contained in “the present.≓ Often it is stated that three-dimensional space and one-dimensional time hare been substituted by four-dimensional space-time in relativity theory, and as a consequence the classical concept of reality, as that which is “present,≓ cannot be retained. Is reality then the (...)
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  31. Diederik Aerts (1994). Constantin Piron at Sixty-Plus: Continuing a Quest for the Understanding of Fundamental Physical Theories and the Pursuit of Their Elaboration. [REVIEW] Foundations of Physics 24 (8):1107-1111.
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  32. Diederik Aerts (1994). Quantum Structures, Separated Physical Entities and Probability. Foundations of Physics 24 (9):1227-1259.
    We prove that if the physical entity S consisting of two separated physical entities S1 and S2 satisfies the axioms of orthodox quantum mechanics, then at least one of the two subentities is a classical physical entity. This theorem implies that separated quantum entities cannot be described by quantum mechanics. We formulate this theorem in an approach where physical entities are described by the set of their states, and the set of their relevant experiments. We also show that the collection (...)
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  33. Diederik Aerts & Thomas Durt (1994). Quantum, Classical and Intermediate: An Illustrative Example. [REVIEW] Foundations of Physics 24 (10):1353-1369.
    We present a model that allows one to build structures that evolve continuously from classical to quantum, and we study the intermediate situations, giving rise to structures that are neither classical nor quantum. We construct the closure structure corresponding to the collection of eigenstate sets of these intermediate situations, and demonstrate how the superposition principle disappears during the transition from quantum to classical. We investigate the validity of the axioms of quantum mechanics for the intermediate situations.
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  34. Liane Gabora & Diederik Aerts, Contextualizing Concepts.
    To cope with problems arising in the description of (1) contextual interactions, and (2) the generation of new states with new properties when quantum entities become entangled, the mathematics of quantum mechanics was developed. Similar problems arise with concepts. We use a generalization of standard quantum mechanics, the mathematical lattice theoretic formalism, to develop a formal description of the contextual manner in which concepts are evoked, used, and combined to generate meaning.
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