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- Aerts, D. (2011). Quantum interference and superposition in cognition: Development of a theory for the disjunction of concepts. In D. Aerts, J. Broekaert, B. D'Hooghe and N. Note (Eds.),
Worldviews, Science and Us: Bridging Knowledge and Its Implications for Our Perspectives of the World(pp. 169-211). Singapore: World Scientific. Archive reference and link: http://uk.arxiv.org/abs/0705.0975. download pdf.

Abstract:We elaborate a theory for the modeling of concepts using the mathematical structure of quantum mechanics. Items and concepts are represented by vectors in the complex Hilbert space of quantum mechanics and membership weights of items are modeled by quantum weights calculated following the quantum rules. We apply this theory to model the disjunction of concepts and show that the predictions of our theory for the membership weights of items with respect to the disjunction of concepts match with great accuracy the results of an experiment conducted by Hampton (1988b). It is the quantum effects of interference and superposition that are at the origin of the effects of overextension and underextension observed by Hampton as deviations from a classical use of the disjunction. We show that the complex numbers of the Hilbert space are essential to obtaining the experimental predictions, i.e. vector space models over real numbers do not provide predictions matching the experimental data. We put forward an explanation of the effects of overextension and underextension by interpreting the quantum model applied to the modeling of the disjunction of concepts.- Aerts, D. (2011). Measuring meaning on the World-Wide Web. In D. Aerts, J. Broekaert, B. D'Hooghe and N. Note (Eds.),
Worldviews, Science and Us: Bridging Knowledge and Its Implications for Our Perspectives of the World(pp. 304-313). Singapore: World Scientific. Archive reference and link: http://arxiv.org/abs/1006.1786. download pdf.

Abstract:We introduce the notion of the 'meaning bond' of a word with respect to another word by making use of the World-Wide Web as a conceptual environment for meaning. This meaning bond is calculated as a value from a formula that expresses the relative appearance of both words in each other neighborhood with respect to the absolute appearance of both words on the whole World-Wide Web. We derive this formula analyzing the comparison of relative appearance with respect to absolute appearance, and prove that the meaning bond is equal to the product of the number of webpages containing both words by the total number of webpages of the World-Wide Web, and dividing the result by the product of the number of webpages for each of the single words. We calculate the meaning bonds for several words and investigate different aspects by looking at specific examples.- Aerts, D., Broekaert, J., Czachor, M. and D'Hooghe, B. (2011). A quantum-conceptual explanation of violations of expected utility in economics.
Proceedings of QI2011-Fifth International Symposium on Quantum Interaction, Robert Gordon University, Aberdeen, Scotland, June 27-29, 2011.Quantum Interaction. Lecture Notes in Computer Science,7052, pp. 192-198. Archive reference and link: http://uk.arxiv.org/abs/1004.2525. doi: 10.1007/978-3-642-24971-6_19. download pdf.

Abstract: The expected utility hypothesis is one of the building blocks of classical economic theory and founded on Savage's Sure-Thing Principle. It has been put forward, e.g. by situations such as the Allais and Ellsberg paradoxes, that real-life situations can violate Savage's Sure-Thing Principle and hence also expected utility. We analyze how this violation is connected to the presence of the 'disjunction effect' of decision theory and use our earlier study of this effect in concept theory to put forward an explanation of the violation of Savage's Sure-Thing Principle, namely the presence of 'quantum conceptual thought' next to 'classical logical thought' within a double layer structure of human thought during the decision process. Quantum conceptual thought can be modeled mathematically by the quantum mechanical formalism, which we illustrate by modeling the Hawaii problem situation, a well-known example of the disjunction effect, and we show how the dynamics in the Hawaii problem situation is generated by the whole conceptual landscape surrounding the decision situation. We analyze the Ellsberg paradox situation, taking into account our hypothesis of the presence of quantum conceptual thought. We put forward a model for the conceptual landscape surrounding the decision situation of the Ellsberg paradox by making use of the data we gathered by conducting an experimental test of the Ellsberg paradox situation. We show how this gives rise to the violation of Savage's Sure-Thing Principle and explain its dynamics.- Aerts, D., Broekaert, J., D'Hooghe, B. and Note, N. (Eds.), (2011).
Worldviews, Science and Us: Bridging Knowledge and Its Implications for Our Perspectives of the World. Singapore: World Scientific.- Aerts, D., Broekaert, J., D'Hooghe, B. and Note, N. (2011). Interdisciplinarity and bridging knowledge. In D. Aerts, J. Broekaert, B. D'Hooghe and N. Note (Eds.),
- Aerts, D., Broekaert, J., D'Hooghe, B. and Sozzo, S. (2011). Quantum structure in economics: Risk versus ambiguity. In D. Aerts, J. Broekaert, B. D'Hooghe and N. Note (Eds.),
- Aerts, D., Broekaert, J. and Gabora, L. (2011). A case for applying an abstracted quantum formalism to cognition.
New Ideas in Psychology,29, pp. 136-146. doi: 10.1016/j.newideapsych.2010.06.002. Archive reference and link: http://uk.arxiv.org/abs/quant-ph/0404068. download pdf.

Abstract: The contextual nature of conscious experience suggests that in order to formally model it we should look to the domain of science where contextuality has been most seriously addressed: quantum mechanics. As in quantum mechanics, conscious experience consists of segments of dynamical evolution, which are not contextual and do not involve resolution of ambiguity or decision, and collapse events, which are context-dependent and involve a decision or the resolution of ambiguity. An abstracted quantum mechanical representation of the entity-context interaction, with its hidden creation of new states, is adapted to the description of the conceptualization process for various cognitive domains. We show that Bell inequalitiesÑthe definitive test for quantum structureÑare violated in the relationship between an abstract concept and instances or exemplars of that concept. We summarize work on a theory of concepts that focuses on how the potentiality of a concept gets actualized through interaction with a context, and how the mathematics of entanglement can be applied to concept combination. A full quantum model is presented for the description of (1) contextually-elicited opinions (as in an opinion pole situation), and (2) the alternating change of cognitive state in the liar paradox.- Aerts, D., Bruza, P., Hou, YX., Jose, J., Melucci, M., Nie, JY., Song, DW. (2011). Quantum theory-inspired search. In E. Giacobino, R. Pfeifer (Eds.),
Proceedings of the 2nd European Future Technologies Conference and Exhibition 2011 (FET 11). Book Series: Procedia Computer Science,7, pp. 278-280. doi: 10.1016/j.procs.2011.09.050.

Abstract: With the huge number and diversity of the users, the advertising products and services, the rapid growth of online multimedia resources, the context of information needs are even more broad and complex. Although research in search engine technology has led to various models over the past three decades, the investigation for effectively integrating the dimensions of context to deploy advanced search technology has been limited due to the lack of a unified modeling and evaluation framework. Quantum Theory (QT) has created new and unprecedented means for communicating and computing. Besides computer science, optics, electronics, physics, QT and search engine technology can be combined: interference in user interaction; entanglement in cognition; superposition in word meaning; non-classical probability in information ranking; complex vector spaces in multimedia search. This paper highlights our recent results on QT-inspired search engine technology.- Aerts, D., Bundervoet, S., Czachor, M., D'Hooghe, B., Gabora L. and Polk, P. (2011). On the foundations of the theory of evolution. In D. Aerts, J. Broekaert, B. D'Hooghe and N. Note (Eds.),

Abstract: In this paper we suggest an alternative to standard neodarwinian evolution theory. The problem is that Darwinism, which sees evolution as a consequence of random variation and natural selection is based on a materialistic - i.e. matter-based - view of science, while matter in itself is considered to be a very complex notion in modern physics. More specifically, on a microlevel, matter and energy are no longer retained within their simple form, and quantum mechanical models are proposed wherein potential form is considered in addition to actual form. We suggest that the starting point of evolution theory cannot be limited to actual variation whereupon is selected, but to variation in the potential of entities according to the context. We are developing formalism, referred to as 'Context driven Actualization of Potential' (CAP), which handles potentiality. CAP describes the evolution of entities as an actualization of potential which is defined by the context each instance of time. As in quantum mechanics, lack of knowledge of the entity, its context, or the interaction between context and entity leads to different forms of indeterminism in relation to the state of the entity. This indeterminism generates a - non-Kolmogorovian - distribution of probabilities that is different from the classical distribution of chance described by Darwinian evolution theory, which stems from a 'actuality focused', i.e. materialistic view of nature. In this paper we present a quantum evolution game that highlights the main differences, which stem from applying our new perspective. As a formal framework, CAP makes it possible to unite different aspects and perspectives on evolution. We conclude that it is more fundamental to consider evolution in general, and hence also biological evolution in specific, as a process of 'context driven actualization of potential', for which its material reduction is only a perspective.- Aerts, D., Czachor, M. and Sozzo, S. (2011). Quantum interaction approach in cognition, artificial intelligence and robotics.
In V. Privman and V. Ovchinnikov (Eds.), IARIA, Proceedings of the Fifth International Conference on Quantum, Nano and Micro Technologies, pp. 35-40. Archive reference and link: http://arxiv.org/abs/1104.3345. download pdf.

Abstract: The mathematical formalism of quantum mechanics has been successfully employed in the last years to model situations in which the use of classical structures gives rise to problematical situations, and where typically quantum effects, such as 'contextuality' and 'entanglement', have been recognized. This 'Quantum Interaction Approach' is briefly reviewed in this paper focusing, in particular, on the quantum models that have been elaborated to describe how concepts combine in cognitive science, and on the ensuing identification of a quantum structure in human thought. We point out that these results provide interesting insights toward the development of a unified theory for meaning and knowledge formalization and representation. Then, we analyze the technological aspects and implications of our approach, and a particular attention is devoted to the connections with symbolic artificial intelligence, quantum computation and robotics.- Aerts, D., de Ronde, C. and D'Hooghe, B. (2011). Compatibility and separability for classical and quantum entanglement. In D. Aerts, J. Broekaert, B. D'Hooghe and N. Note (Eds.),

Abstract: We study the concepts of compatibility and separability and their implications for quantum and classical systems. These concepts are illustrated on a macroscopic model for the singlet state of a quantum system of two entangled spin 1/2 with a parameter reflecting indeterminism in the measurement procedure. By varying this parameter we describe situations from quantum, intermediate to classical and study which tests are compatible or separated. We prove that for classical deterministic systems the concepts of separability and compatibility coincide, but for quantum systems and intermediate systems these concepts are generally different. More specifically, equal physical constraints in the model, which for classical deterministic measurements lead to non-separability 'and' non-compatibility of the measurements, give rise to compatible measurements that are non-separated whenever indeterminism is introduced. As a consequence, compatible measurements that are non-separated, and hence violate Bell's inequalities, can only be realized in the presence of indeterminism.- Aerts, D. and D'Hooghe, B. (2011). Potentiality states: Quantum versus classical emergence. In D. Aerts, J. Broekaert, B. D'Hooghe and N. Note (Eds.),

Abstract: We identify emergence with the existence of states of potentiality related to relevant physical quantities. We introduce the concept of 'potentiality state' operationally and show how it reduces to 'superposition state' when standard quantum mechanics can be applied. We consider several examples to illustrate our approach, and define the potentiality states giving rise to emergence in each example. We prove that Bell inequalities are violated by the potentiality states in the examples, which, taking into account Pitowsky's theorem, experimentally indicates the presence of quantum structure in emergence. In the first example emergence arises because of the many ways water can be subdivided into different vessels. In the second example, we put forward a full quantum description of the Liar paradox situation, and identify the potentiality states, which in this case turn out to be superposition states. In the example of the soccer team, we show the difference between classical emergence as stable dynamical pattern and emergence defined by a potentiality state, and show how Bell inequalities can be violated in the case of highly contextual experiments.- Aerts, D., D'Hooghe, B., Pinxten, H. and Wallerstein, I. (Eds.), (2011).
Worldviews, Science and Us: Interdisciplinary Perspectives on Worlds, Cultures and Society. Singapore: World Scientific.- Aerts, D., D'Hooghe, B., Pinxten, H. and Wallerstein, I. (2011). Interdisciplinary perspectives on worlds, cultures and society. In D. Aerts, B. D'Hooghe, R. Pinxten and I. Wallerstein (Eds.),
Worldviews, Science and Us: Interdisciplinary Perspectives on Worlds, Cultures and Society (pp 1-4). Singapore: World Scientific.- Aerts, D., D'Hooghe, B. and Sioen, M. (2011). Quantum axiomatics: Topological properties and classical properties of state property systems.
International Journal of Theoretical Physics,50, pp. 3635-3645. doi: 10.1007/s10773-011-0885-9.

Abstract: The definition of 'classical state' from (Aerts in K. Engesser, D. Gabbay and D. Lehmann (Eds.), Handbook of Quantum Logic and Quantum Structures. Elsevier, Amsterdam, 2009), used e.g. in Aerts et al. (http://arxiv.org/abs/quant-ph/0503083, 2010) to prove a decomposition theorem internally in the language of State Property Systems, presupposes as an additional datum an orthocomplementation on the property lattice of a physical system. In this paper we argue on the basis of the (epsilon,d)-model on the Poincare sphere that a notion of topologicity for states can be seen as an alternative (operationally foundable) classicality notion in the absence of an orthocomplementation, and compare it to the known and operationally founded concept of classicality.- Aerts, D., D'Hooghe, B. and Sozzo, S. (2011). A quantum cognition analysis of the Ellsberg paradox.
Proceedings of QI2011-Fifth International Symposium on Quantum Interaction, Robert Gordon University, Aberdeen, Scotland, June 27-29, 2011.Quantum Interaction. Lecture Notes in Computer Science,7052, pp. 95-104. Archive reference and link: http://arxiv.org/abs/1104.1459. doi: 10.1007/978-3-642-24971-6_10. download pdf.

Abstract: The 'expected utility hypothesis' is one of the foundations of classical approaches to economics and decision theory and Savage's 'Sure-Thing Principle' is a fundamental element of it. It has been put forward that real-life situations exist, illustrated by the 'Allais' and 'Ellsberg paradoxes', in which the Sure-Thing Principle is violated, and where also the expected utility hypothesis does not hold. We have recently presented strong arguments for the presence of a double layer structure, a 'classical logical' and a 'quantum conceptual', in human thought and that the quantum conceptual mode is responsible of the above violation. We consider in this paper the Ellsberg paradox, perform an experiment with real test subjects on the situation considered by Ellsberg, and use the collected data to elaborate a model for the conceptual landscape surrounding the decision situation of the paradox. We show that it is the conceptual landscape which gives rise to a violation of the Sure-Thing Principle and leads to the paradoxical situation discovered by Ellsberg.- Aerts, D., Gabora, L., Sozzo, S. and Veloz, T. (2011). Quantum structure in cognition: Fundamentals and applications.
In V. Privman and V. Ovchinnikov (Eds.), IARIA, Proceedings of the Fifth International Conference on Quantum, Nano and Micro Technologies, pp. 57-62. Archive reference and link: http://arxiv.org/abs/1104.3344. download pdf.

Abstract: Experiments in cognitive science and decision theory show that the ways in which people combine concepts and make decisions cannot be described by classical logic and probability theory. This has serious implications for applied disciplines such as information retrieval, artificial intelligence and robotics. Inspired by a mathematical formalism that generalizes quantum mechanics the authors have constructed a contextual framework for both concept representation and decision making, together with quantum models that are in strong alignment with experimental data. The results can be interpreted by assuming the existence in human thought of a double-layered structure, a 'classical logical thought' and a 'quantum conceptual thought', the latter being responsible of the above paradoxes and nonclassical effects. The presence of a quantum structure in cognition is relevant, for it shows that quantum mechanics provides not only a useful modeling tool for experimental data but also supplies a structural model for human and artificial thought processes. This approach has strong connections with theories formalizing meaning, such as semantic analysis, and has also a deep impact on computer science, information retrieval and artificial intelligence. More specifically, the links with information retrieval are discussed in this paper.- Aerts, D. and Sozzo, S. (2011). Quantum structure in cognition: Why and how concepts are entangled.
Proceedings of QI2011-Fifth International Symposium on Quantum Interaction, Robert Gordon University, Aberdeen, Scotland, June 27-29, 2011.Quantum Interaction. Lecture Notes in Computer Science,7052, pp. 116-127. Archive reference and link: http://arxiv.org/abs/1104.1322. doi: 10.1007/978-3-642-24971-6_12. download pdf.

Abstract: One of us has recently elaborated a theory for modelling concepts that uses the state context property (SCoP) formalism, i.e. a generalization of the quantum formalism. This formalism incorporates context into the mathematical structure used to represent a concept, and thereby models how context influences the typicality of a single exemplar and the applicability of a single property of a concept. The notion of 'state of a concept' is introduced to account for this contextual influence, which proposes a solution for the 'Pet-Fish problem' and several difficulties occurring in concept theory. Then, a quantum model has been worked out which reproduces the membership weights of several exemplars of concepts and their combinations. We show in this paper that a further relevant effect appears in a natural way whenever two or more concepts combine, namely, 'entanglement'. The presence of entanglement is explicitly revealed by considering a specific example with two concepts, constructing some Bell's inequalities for this example, testing them in a real experiment with test subjects, and finally proving that Bell's inequalities are violated in this case. We show that the intrinsic and unavoidable character of entanglement can be explained in terms of the weights of the exemplars of the combined concept with respect to the weights of the exemplars of the component concepts, and elaborate a concrete quantum model for the proposed example.- Patyk, A., Czachor, M. and Aerts, D. (2011). A comparison of geometric analogues of holographic reduced representations, original holographic reduced representations and binary spatter codes.
Proceedings of the Federated Conference on Computer Science and Information Systems (FedCSIS), Szczecin, Poland, 18-21 September, 2011, pp. 221-228.

Abstract: Geometric Analogues of Holographic Reduced Representations (GA HRR) employ role-filler binding based on geometric products. Atomic objects are real-valued vectors in n-dimensional Euclidean space and complex statements belong to a hierarchy of multivectors. The paper reports a battery of tests aimed at comparison of GA HRR with Holographic Reduced Representation (HRR) and Binary Spatter Codes (BSC). Firstly, we perform a test of GA HRR which is analogous to the one proposed by Plate. Plate's simulation involved several thousand 512-dimensional vectors stored in clean-up memory. The purpose was to study efficiency of HRR but also to provide a counterexample to claims that role-filler representations do not permit one component of a relation to be retrieved given the others. We repeat Plate's test on a continuous version of GA HRR - GAc (as opposed to its discrete version) and compare the results with the original HRR and BSC. The object of the test is to construct statements concerning multiplication and addition. For example, "2á3 = 6" is constructed as times2,3 = times+operand*(num2 + num3)+result*num6. To look up this vector one then constructs a similar statement with one of the components missing and checks whether it points correctly to times2,3. We concentrate on comparison of recognition percentage for the three models for comparable data size, rather than on the time taken to achieve high percentage. Results show that the best models for storing and recognizing multiple similar statements are GAc and Binary Spatter Codes with recognition percentage highly above 90.- Patyk, A., Czachor, M. and Aerts, D. (2011). Distributed representations based on geometric algebra: The continuous model.
Informatica,35, pp. 407-417.

Abstract: Authors revise the concept of a distributed representation of data as well as two previously developed models: Holographic Reduced Representation (HRR) and Binary Spatter Codes (BSC). A Geometric Analogue (GAc Ñ "c" stands for continuous as opposed to its discrete version) of HRR is introduced Ð it employs role-filler binding based on geometric products. Atomic objects are real-valued vectors in n-dimensional Euclidean space while complex data structures belong to a hierarchy of multivectors. The paper reports on a test aimed at comparison of GAc with HRR and BSC. The test is analogous to the one proposed by Tony Plate in the mid 90s. We repeat PlateÕs test on GAc and compare the results with the original HRR and BSCÑwe concentrate on comparison of recognition percentage for the three models for comparable data size, rather than on the time taken to achieve high percentage. Results show that the best models for storing and recognizing multiple similar structures are GAc and BSC with recognition percentage highly above 90. The paper ends with remarks on perspective applications of geometric algebra to quantum algorithms.- Veloz, T., Gabora, L., Eyjolfson, J. and Aerts, D. (2011). Toward a formal model of the shifting relationship between concepts and contexts during associative thought.
Proceedings of QI2011-Fifth International Symposium on Quantum Interaction, Robert Gordon University, Aberdeen, Scotland, June 27-29, 2011.Quantum Interaction. Lecture Notes in Computer Science,7052, pp. 25-34. doi: 10.1007/978-3-642-24971-6_4.

Abstract: The quantum inspired State Context Property (SCOP) theory of concepts is unique amongst theories of concepts in offering a means of incorporating that for each concept in each different context there are an unlimited number of exemplars, or states, of varying degrees of typicality. Working with data from a study in which participants were asked to rate the typicality of exemplars of a concept for different contexts, and introducing a state-transition threshold, we built a SCOP model of how states of a concept arise differently in associative versus analytic (or divergent and convergent) modes of thought. Introducing measures of expected typicality for both states and contexts, we show that by varying the threshold, the expected typicality of different contexts changes, and seemingly atypical states can become typical. The formalism provides a pivotal step toward a formal explanation of creative thought processes.

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

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