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- Aerts, D. (2013). Quantum and concept combination, entangled measurements and prototype theory. To appear in
Topics in Cognitive Science. Archive reference and link: http://arxiv.org/abs/1303.2430. download pdf.

Abstract:We extend a quantum model in Hilbert space developed in Aerts (2007a) into a quantum field theoric model in Fock space for the modeling of the combination of concepts. Items and concepts are represented by vectors in Fock space and membership weights of items are modeled by quantum probabilities. We apply this theory to model the disjunction of concepts and show that the predictions of our theory for the membership weights of items regarding the disjunction of concepts match with great accuracy the complete set of results of an experiment conducted by Hampton (1988b). It are the quantum effects of interference and superposition of that are at the origin of the effects of overextension and underextension observed by Hampton as deviations from a classical use of the disjunction. It is essential for the perfect matches we obtain between the predictions of the quantum field model and Hampton's experimental data that items can be in superpositions of `different numbers states' which proves that the genuine structure of quantum field theory is needed to match predictions with experimental data.- Aerts, D. (2013). La mecànica cuántica y la conceptualidad: Sobre materia, historias, semántica y espacio-tiempo.
Scientiae Studia,11, pp. 75-100. download pdf. doi: 10.1590/S1678-31662013000100004. (translated from: Aerts, D. (2012). Quantum theory and conceptuality: Matter, stories, semantics and space-time. Archive reference and link: http://arxiv.org/abs/1110.4766. download pdf.)

Abstract:We elaborate the new interpretation of quantum theory that we recently proposed, according to which quantum particles are considered conceptual entities mediating between pieces of ordinary matter which are considered to act as memory structures for them. Our aim is to identify what is the equivalent for the human cognitive realm of what physical space-time is for the realm of quantum particles and ordinary matter. For this purpose, we identify the notion of 'story' as the equivalent within the human cognitive realm of what ordinary matter is in the physical quantum realm, and analyze the role played by the logical connectives of disjunction and conjunction with respect to the notion of locality. Similarly to what we have done in earlier investigations on this new quantum interpretation, we use the specific cognitive environment of the World-Wide Web to elucidate the comparisons we make between the human cognitive realm and the physical quantum realm.- Aerts, D., Broekaert, J., Gabora, L. and Sozzo, S. (2013). Quantum structure and human thought.
Behavioral and Brain Sciences,36, pp. 274-277. doi: 10.1017/S0140525X12002841. download pdf.

Abstract: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.- Aerts, D., Broekaert, J, Sozzo, S. and Veloz, T. (2013). Meaning-focused and quantum-inspired information retrieval. Accepted for publication in
Lecture Notes in Computer Science. Archive reference and link: http://arxiv.org/abs/1304.0104. download pdf.

Abstract: In recent years, quantum-based methods have promisingly integrated the traditional procedures in information retrieval (IR) and natural language processing (NLP). Inspired by our research on the identification and application of quantum structures in cognition, we put forward a new 'quantum meaning based' framework for structured query retrieval in text corpora and standardized testing corpora. This scheme for IR rests on 'entities of meaning', e.g., concepts and their combinations, and 'documents', i.e. traces of entities of meaning, as basic entities. The meaning content of the latter is then reconstructed in terms of the meaning content of the former through an 'inverse problem'. The advantages with respect to traditional approaches, such as Latent Semantic Analysis (LSA), are finally discussed by means of concrete examples.- Aerts, D., Broekaert, J, Sozzo, S. and Veloz, T. (2013). The quantum challenge in concept theory and natural language processing. In E. G. Lasker (Ed.),
Proceedings of the 25th International Conference on System Research, Informatics & Cybernetics, pp. 13-17, IIAS. Archive reference and link: http://arxiv.org/abs/1306.2838. download pdf.

Abstract: The mathematical formalism of quantum theory has been successfully used in human cognition to model decision processes and to deliver representations of human knowledge. As such, quantum cognition inspired tools have improved technologies for Natural Language Processing and Information Retrieval. In this paper, we overview the quantum cognition approach developed in our Brussels team during the last two decades, specifically our identification of quantum structures in human concepts and language, and the modeling of data from psychological and corpus-text-based experiments. We discuss our quantum-theoretic framework for concepts and their conjunctions/disjunctions in a Fock-Hilbert space structure, adequately modeling a large amount of data collected on concept combinations. Inspired by this modeling, we put forward elements for a quantum contextual and meaning-based approach to information technologies in which 'entities of meaning' are inversely reconstructed from texts, which are considered as traces of these entities' states.- Aerts, D., Czachor, M., Kuna, M. and Sozzo, S. (2013). Systems, environments, and soliton rate equations: A non-Kolmogorovian framework for population dynamics.
Ecological Modelling,267, pp. 80-92. doi: 10.1016/j.ecolmodel.2013.07.010. Archive reference and link: http://arxiv.org/abs/1303.0281. download pdf.

Abstract:Soliton rate equations are based on non-Kolmogorovian models of probability and naturally include autocatalytic processes. The formalism is not widely known but has great unexplored potential for applications to systems interacting with environments. Beginning with links of contextuality to non-Kolmogorovity we introduce the general formalism of soliton rate equations and work out explicit examples of subsystems interacting with environments. Of particular interest is the case of a soliton autocatalytic rate equation coupled to a linear conservative environment, a formal way of expressing seasonal changes. Depending on strength of the system-environment coupling we observe phenomena analogous to hibernation or even complete blocking of decay of a population.- Aerts, D., Gabora, L. and Sozzo, S. (2013). Concepts and their dynamics: A quantum-theoretic modeling of human thought. Topics in Cognitive Science,
5, pp. 737-772. doi: 10.1111/tops.12042. Archive reference and link: http://arxiv.org/abs/1206.1069. download pdf.

Abstract: 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, i.e. prototype theory, exemplar theory and theory theory. We ponder about the question why quantum theory performs so well in its modeling of human concepts, and shed light on this question by analyzing the role of complex amplitudes, showing how they allow to describe interference in the statistics of measurement outcomes, while in the traditional theories statistics of outcomes originates in classical probability weights, without the possibility of interference. The relevance of complex numbers, the appearance of entanglement, and the role of Fock space in explaining contextual emergence, all as unique features of the quantum modeling, are explicitly revealed in this paper by analyzing human concepts and their dynamics.- Aerts, D. and Sozzo, S. (2013). Quantum entanglement in concept combinations. Accepted for publication in
International Journal of Theoretical Physics. Archive reference and link: http://arxiv.org/abs/1302.3831. download pdf.

Abstract: Research in the application of quantum structures to cognitive science confirms that these structures quite systematically appear in the dynamics of concepts and their combinations and quantum-based models faithfully represent experimental data of situations where classical approaches are problematical. In this paper, we analyze the data we collected in an experiment on a specific conceptual combination, showing that Bell's inequalities are violated in the experiment. We present a new refined entanglement scheme to model these data within standard quantum theory rules, where 'entangled measurements and entangled evolutions' occur, in addition to the expected 'entangled states', and present a full quantum representation in complex Hilbert space of the data. This stronger form of entanglement in measurements and evolutions might have relevant applications in the foundations of quantum theory, as well as in the interpretation of nonlocality tests. It could indeed explain some non-negligible 'anomalies' identified in EPR-Bell experiments.- Aerts, D. and Sozzo, S. (2013). Entanglement zoo I: Foundational and structural aspects. Accepted for publication in
Lecture Notes in Computer Science. Archive reference and link: http://arxiv.org/abs/1304.0100. download pdf.

Abstract: We put forward a general classification for a structural description of the entanglement present in compound entities experimentally violating Bell's inequalities, making use of a new entanglement scheme that we developed recently. Our scheme, although different from the traditional one, is completely compatible with standard quantum theory, and enables quantum modeling in complex Hilbert space for different types of situations. Namely, situations where entangled states and product measurements appear ('customary quantum modeling'), and situations where states and measurements and evolutions between measurements are entangled ('nonlocal box modeling', 'nonlocal non-marginal box modeling'). The role played by Tsirelson's bound and marginal distribution law is emphasized. Specific quantum models are worked out in detail in complex Hilbert space within this new entanglement scheme.- Aerts, D. and Sozzo, S. (2013). Entanglement zoo II: Examples in physics and cognition. Accepted for publication in
Lecture Notes in Computer Science. Archive reference and link: http://arxiv.org/abs/1304.0102. download pdf.

Abstract: We have recently presented a general scheme enabling quantum modeling of different types of situations that violate Bell's inequalities. In this paper, we specify this scheme for a combination of two concepts. We work out a quantum Hilbert space model where 'entangled measurements' occur in addition to the expected 'entanglement between the component concepts', or 'state entanglement'. We extend this result to a macroscopic physical entity, the 'connected vessels of water', which maximally violates Bell's inequalities. We enlighten the structural and conceptual analogies between the cognitive and physical situations which are both examples of a nonlocal non-marginal box modeling in our classification.- Aerts, D. and Sozzo, S. (2013). General quantum Hilbert Space modeling scheme for entanglement. In V. Ovchinnikov and P. Dini (Eds.),
Proceedings of the Seventh International Conference on Quantum, Nano and Micro Technologies (IARIA, 2013), pp. 25-31. Archive reference and link: http://arxiv.org/abs/1304.3733. download pdf.

Abstract: We work out a classification scheme for quantum modeling in Hilbert space of any kind of composite entity violating Bell's inequalities and exhibiting entanglement. Our theoretical framework includes situations with entangled states and product measurements ('customary quantum situation'), and also situations with both entangled states and entangled measurements ('nonlocal box situation', 'nonlocal non-marginal box situation'). We show that entanglement is structurally a joint property of states and measurements. Furthermore, entangled measurements enable quantum modeling of situations that are usually believed to be 'beyond quantum'. Our results are also extended from pure states to quantum mixtures.- Aerts, D. and Sozzo, S. (2013). Modeling concept combinations in a quantum-theoretic framework. In S. Roy (Ed.),
Fourth International Conference on Cognitive Neurodynamics (ICCN 2013). Archive reference and link: http://arxiv.org/abs/1401.3626. download pdf.

Abstract: We present modeling for conceptual combinations which uses the mathematical formalism of quantum theory. Our model faithfully describes a large amount of experimental data collected by different scholars on concept conjunctions and disjunctions. Furthermore, our approach sheds a new light on long standing drawbacks connected with vagueness, or fuzziness, of concepts, and puts forward a completely novel possible solution to the 'combination problem' in concept theory. Additionally, we introduce an explanation for the occurrence of quantum structures in the mechanisms and dynamics of concepts and, more generally, in cognitive and decision processes, according to which human thought is a well structured superposition of a `logical thought' and a 'conceptual thought', and the latter usually prevails over the former, at variance with some widespread beliefs.- Aerts, D., Sozzo, S. and Tapia, J. (2013). Identifying quantum structures in the Ellsberg paradox. Accepted for publication in
International Journal of Theoretical Physics. Archive reference and link: http://arxiv.org/abs/1302.3850. download pdf.

Abstract: Empirical evidence has confirmed that quantum effects systematically occur also outside the microscopic domain, while quantum structures satisfactorily model various situations in several areas of science, including biological, cognitive and social processes. In this paper, we elaborate a quantum mechanical model which faithfully describes the Ellsberg paradox in economics, showing that the mathematical formalism of quantum mechanics is capable to represent the ambiguity present in this kind of situations, because of the presence of contextuality. Then, we analyze the data collected in a concrete experiment we performed on the Ellsberg paradox and work out a complete representation of them in complex Hilbert space. We prove that the self-adjoint operators representing the two processes of decision of our test subjects related to the two bets cannot be commuting operators. This shows that the presence of quantum structure is genuine, and due to the statistics following from our experimental data. It also proves that no classical probabilistic model is possible for these collected experimental data on the Ellsberg conceptual situation. Our approach sheds light on `ambiguity laden' decision processes in economics and decision theory, and allows to deal with different Ellsberg-type generalizations, e.g., the Machina paradox.

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

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