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- Aerts, D. (2009). Quantum structure in cognition.
Journal of Mathematical Psychology,53, 314-348. Archive reference and link: http://uk.arxiv.org/abs/0805.3850. doi:10.1016/j.jmp.2009.04.005

Abstract:The broader scope of our investigations is the search for the way in which concepts and their combinations carry and influence meaning and what this implies for human thought. More specifically, we examine the use of the mathematical formalism of quantum mechanics as a modeling instrument and propose a general mathematical modeling scheme for the combinations of concepts. We point out that quantum mechanical principles, such as superposition and interference, are at the origin of specific effects in cognition related to concept combinations, such as the guppy effect and the overextension and underextension of membership weights of items. We work out a concrete quantum mechanical model for a large set of experimental data of membership weights with overextension and underextension of items with respect to the conjunction and disjunction of pairs of concepts, and show that no classical model is possible for these data. We put forward an explanation by linking the presence of quantum aspects that model concept combinations to the basic process of concept formation. We investigate the implications of our quantum modeling scheme for the structure of human thought, and show the presence of a two-layer structure consisting of a classical logical layer and a quantum conceptual layer. We consider connections between our findings and phenomena such as the disjunction effect and the conjunction fallacy in decision theory, violations of the sure thing principle, and the Allais and Elsberg paradoxes in economics.- Aerts, D. (2009). Quantum axiomatics. In K. Engesser, D. Gabbay and D. Lehmann (Eds.),
Handbook of Quantum Logic and Quantum Structures,. Amsterdam: Elsevier.

Abstract: We present an axiomatic and operational theory of quantum mechanics. The theory is founded on the axiomatic and operational approach started in Geneva mainly by Constantin Piron and his students and collaborators and developed further in Brussels by myself and different students and collaborators. A physical entity, which a priori can be a classical entity or a quantum entity or a combination of both, is described by means of its set of states, its set of properties and a physical notion of `actuality of a property the entity being in a state'. This leads to the mathematical structure of a state property space. We introduce seven axioms such that if satisfied the state property space can be represented by the direct union over a classical state space of irreducible state property spaces, where each one of the irreducible state property spaces is a Hilbert space state property space of standard quantum mechanics, over the real, complex or quaternionic numbers. The axioms are introduced in an as much as possible operational way, such that we can analyze their physical meaning.- Aerts, D. (2009). Operational quantum mechanics, quantum axiomatics and quantum structures. In D. Greenberger, K. Hentschel and F. Wienert (Eds.),
Compendium of Quantum Physics Concepts, Experiments, History and Philosophy(pp. 434-440). Berlin, Heidelberg: Springer. Archive reference and link: http://uk.arxiv.org/abs/0811.2516. doi: 10.1007/978-3-540-70626-7.- Aerts, D. (2009). Quantum particles as conceptual entities: A possible explanatory framework for quantum theory.
Foundations of Science,14, 361-411. Archive reference and link: http://uk.arxiv.org/abs/1004.2530, doi: 10.1007/s10699-009-9166-y.

Abstract: 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 individuality in the light of this new interpretation, and we put forward a specific explanation and understanding of these aspects. The basic hypothesis of our framework gives rise in a natural way to a Heisenberg uncertainty principle which introduces an understanding of the general situation of Ôthe one and the manyÕ in quantum physics. A specific view on macro and micro different from the common one follows from the basic hypothesis and leads to an analysis of SchršdingerÕs Cat paradox and the measurement problem different from the existing ones. We reflect about the influence of this new quantum interpretation and explanatory framework on the global nature and evolutionary aspects of the world and human worldviews, and point out potential explanations for specific situations, such as the generation problem in particle physics, the confinement of quarks and the existence of dark matter.- Aerts, D., Aerts, S. and Gabora, L. (2009). Experimental evidence for quantum structure in cognition. In P. D. Bruza, D. Sofge, W. Lawless, C. J. van Rijsbergen and M. Klusch (Eds.),
Proceedings of QI 2009-Third International Symposium on Quantum Interaction, Book series: Lecture Notes in Computer Science,5494, pp. 59-70. Berlin, Heidelberg: Springer. Archice reference and link: http://uk.arxiv.org/abs/0810.5290. doi: 10.1007/978-3-642-00834-4_7.

Abstract: We proof a theorem that shows that a collection of experimental data of membership weights of items with respect to a pair of concepts and its conjunction cannot be modeled within a classical measure theoretic weight structure in case the experimental data contain the effect called overextension. Since the effect of overextension, analogue to the well-known guppy effect for concept combinations, is abundant in all experiments testing weights of items with respect to pairs of concepts and their conjunctions, our theorem constitutes a no-go theorem for classical measure structure for common data of membership weights of items with respect to concepts and their combinations. We put forward a simple geometric criterion that reveals the non classicality of the membership weight structure and use experimentally measured membership weights estimated by subjects in experiments to illustrate our geometrical criterion. The violation of the classical weight structure is similar to the violation of the well-known Bell inequalities studied in quantum mechanics, and hence suggests that the quantum formalism and hence the modeling by quantum membership weights can accomplish what classical membership weights cannot do.- Aerts, D. and D'Hooghe, B. (2009). Classical logical versus quantum conceptual thought: Examples in economics, decision theory and concept theory. In P. D. Bruza, D. Sofge, W. Lawless, C. J. van Rijsbergen and M. Klusch (Eds.),
Proceedings of QI 2009-Third International Symposium on Quantum Interaction, Book series: Lecture Notes in Computer Science,5494, pp. 128-142. Berlin, Heidelberg: Springer. Archice reference and link: http://uk.arxiv.org/abs/0810.5332. doi: 10.1007/978-3-642-00834-4_12.

Abstract: Inspired by a quantum mechanical formalism to model concepts and their disjunctions and conjunctions, we put forward in this paper a specific hypothesis. Namely that within human thought two superposed layers can be distinguished: (i) a layer given form by an underlying classical deterministic process, incorporating essentially logical thought and its indeterministic version modeled by classical probability theory; (ii) a layer given form under influence of the totality of the surrounding conceptual landscape, where the different concepts figure as individual entities rather than (logical) combinations of others, with measurable quantities such as 'typicality', 'membership', 'representativeness', 'similarity', 'applicability', 'preference' or 'utility' carrying the influences. We call the process in this second layer 'quantum conceptual thought', which is indeterministic in essence, and contains holistic aspects, but is equally well, although very differently, organized than logical thought. A substantial part of the 'quantum conceptual thought process' can be modeled by quantum mechanical probabilistic and mathematical structures. We consider examples of three specific domains of research where the effects of the presence of quantum conceptual thought and its deviations from classical logical thought have been noticed and studied, i.e. economics, decision theory, and concept theories and which provide experimental evidence for our hypothesis.- Aerts, D., Czachor, M. and De Moor, B. (2009). Geometric analogue of holographic reduced representation.
Journal of Mathematical Psychology,53, 389-398. Archive reference and link: http://uk.arxiv.org/abs/0710.2611. doi: 10.1016/j.jmp.2009.02.005

Abstract: Holographic reduced representations (HRRs) are distributed representations of cognitive structures based on superpositions of convolution-bound n-tuples. Restricting HRRs to n-tuples consisting of ±1 one reinterprets the variable binding as a representation of the additive group of binary n-tuples with addition modulo 2. Since convolutions are not defined for vectors, the HRRs cannot be directly associated with geometric structures. Geometric analogues of HRRs are obtained if one considers a projective representation of the same group in the space of blades (geometric products of basis vectors) associated with an arbitrary n-dimensional Euclidean (or pseudo-Euclidean) space. Switching to matrix representations of Clifford algebras one can always turn a geometric analogue of HRR into a form of matrix distributed representation. In typical applications the resulting matrices are sparse, so that the matrix representation is less efficient than the representation directly employing the rules of geometric algebra. A yet more efficient procedure is based on 'projected products', a hierarchy of geometrically meaningful n-tuple multiplication rules obtained by combining geometric products with projections on relevant multivector sub-spaces. In terms of dimensionality the geometric analogues of HRRs are in between holographic and tensor-product representations.- Aerts, D., Czachor, M. and Orlowski, L. (2009). Teleportation of geometric structures in 3D,
Journal of Physics A: Mathematical and Theoretical,42, 135307. Archive reference and link: http://uk.arxiv.org/abs/0809.0579. doi: 10.1088/1751-8113/42/13/135307.

Abstract: Simplest quantum teleportation algorithms can be represented in geometric terms in spaces of dimensions 3 (for real state-vectors) and 4 (for complex state-vectors). The geometric representation is based on geometric-algebra coding, a geometric alternative to the tensor-product coding typical of quantum mechanics. We discuss all the elementary ingredients of the geometric version of the algorithm: Geometric analogs of states and controlled Pauli gates. Fully geometric presentation is possible if one employs a nonstandard representation of directed magnitudes, formulated in terms of colors defined via stereographic projection of a color wheel, and not by means of directed volumes.- Gabora, L. and Aerts, D. (2009). A model of the emergence and evolution of integrated worldviews.
Journal of Mathematical Psychology,53, 434-451. doi:10.1016/j.jmp.2009.06.004.

Abstract: It is proposed that the ability of humans to flourish in diverse environments and evolve complex cultures reflects the following two underlying cognitive transitions. The transition from the coarse-grained associative memory of Homo habilis to the fine-grained memory of Homo erectus enabled limited representational redescription of perceptually similar episodes, abstraction, and analytic thought, the last of which is modeled as the formation of states and of lattices of properties and contexts for concepts. The transition to the modern mind of Homo sapiens is proposed to have resulted from onset of the capacity to spontaneously and temporarily shift to an associative mode of thought conducive to interaction amongst seemingly disparate concepts, modeled as the forging of conjunctions resulting in states of entanglement. The fruits of associative thought became ingredients for analytic thought, and vice versa. The ratio of associative pathways to concepts surpassed a percolation threshold resulting in the emergence of a self-modifying, integrated internal model of the world, or worldview.- Meurs, P., Note, N and Aerts, D. (2009). This world without another. On Jean-Luc Nancy and 'la mondialisation'.
Journal of Critical Globalization Studies,1, 31-46.

Abstract: In this paper, we turn to the philosophy of Jean-Luc Nancy. In his work 'La Creation du Monde ou la Mondialisation' of 2002 the French philosopher analyses the process of globalisation. Rather than denoting a new homogeneity, the term refers to a world horizon characterized in its inter- palpable multiplicity of cultural, socio-economical, ideological and politico-moral content. According to Nancy, globalisation refers to ag-glome-ration: the decay of what once was a globe and now nothing more than a glome. On the one hand, Nancy indicates that the world has changed by an unknown increase of techno-science, the worsening of inequalities between growing populations and by the changing and disappearing of given certainties, views and identities of the world and of man. On a large scale, this deformation is due to the relation between the capitalist evolution and the capitalising of worldviews. On the other hand, due to the inter-palpability of the multiplicity, this means that on our planet there is only space for one world. The world gradually becomes the only world. In this paper we will investigate what Nancy means with the becoming-world of the world and how this relates to our being in the world. For Nancy globalisation reveals two possible destinies of our relation with the world. In 'La Creation du Monde ou la Mondialisation' he discerns globalisation from mondialisation to analyze these two possibilities. We will investigate this distinction of Nancy and its consequences for everyday life.

1981, 1982, 1983, 1984, 1985, 1986, 1987, 1988, 1989, 1990,

1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000,