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- Aerts, D. (2002). The unification of personal presents: a dialogue of different world views.
International Readings on Theory, History and Philosophy of Culture: Ontology of Dialogue,12, pp. 63-82.

Abstract:We want to analyse in this article the process of ontological unification of personal world views to a common world view. The hypothesis that we want to put forward is that this process is badly understood and its misunderstandings are at the origin of some of the deep paradoxes about the nature of reality. The title might suggest that we will concentrate mostly on the process of unification that takes place within the psycho- cognitive regions of reality, namely how the psychological, moral, ethical, etc ... aspects of personal world views interact towards the formation of a common world view. This is however not true. We do not underestimate the importance of the process of unification in the psycho-cognitive region, but we will concentrate in this article on a more primitive region of reality, namely the physical region, where the process of unification takes place at early age, and we have mostly forgotten about its nature, which is at the origin of some of the misunderstandings that exist, and the paradoxes that are a consequence of these misunderstandings.- Aerts, D. (2002). Being and change: foundations of a realistic operational formalism. In D. Aerts, M. Czachor and T. Durt (Eds.),
Probing the Structure of Quantum Mechanics: Nonlinearity, Nonlocality, Probability and Axiomatics(pp. 71-110). Singapore: World Scientific. Archive reference and link: http://uk.arxiv.org/abs/quant-ph/0205164.

Abstract: The aim of this article is to represent the general description of an entity by means of its states, contexts and properties. The entity that we want to describe does not necessarily has to be a physical entity, but can also be an entity of a more abstract nature, for example a concept, or a cultural artifact, or the mind of a person, etc..., which means that we aim at very general description. The effect that a context has on the state of the entity plays a fundamental role, which means that our approach is intrinsically contextual. The approach is inspired by the mathematical formalisms that have been developed in axiomatic quantum mechanics, where a specific type of quantum contextuality is modelled, but, because in general states also influence context -- which is not the case in quantum mechanics -- we need a more general setting than the one used there. Our focus on context as a fundamental concept makes it possible to unify 'dynamical change' and 'change under influence of measurement', which makes our approach also more general and more powerful than the traditional quantum axiomatic approaches. For this reason an experiment (or measurement) is introduced as a specific kind of context. Mathematically we introduce a state context property system as the structure to describe an entity by means of its states, contexts and properties. We also strive from the start to a the categorical setting, a way that has been investigated extensively in earlier work, and hence, from a merological covariance principle, we derive the morphisms between state context property systems and introduce the categorySCOPwith elements the state context property systems and morphisms the ones that we derived from this merological covariance principle. We introduce property completeness and state completeness and study the operational foundation of the formalism.- Aerts, D. (2002). Reality and probability: introducing a new type of probability calculus. In D. Aerts, M. Czachor and T. Durt (Eds.),
Probing the Structure of Quantum Mechanics: Nonlinearity, Nonlocality, Probability and Axiomatics(pp. 205-229). Singapore: World Scientific. Archive reference and link: http://uk.arxiv.org/abs/quant-ph/0205165.

Abstract:We consider a conception of reality that is the following: An object is 'real' if we know that if we would try to test whether this object is present, this test would give us the answer 'yes' with certainty. The knowledge about this certainty we gather from our overall experience with the world. If we consider a conception of reality where probability plays a fundamental role, which we should do if we want to incorporate the microworld into our reality, it can be shown that standard probability theory is not well suited to substitute 'certainty' by means of 'probability equal to 1'. We analyze the different problems that arise when one tries to push standard probability to deliver a conception of reality as the one we advocate. The analysis of these problems lead us to propose a new type of probability theory that is a generalization of standard probability theory. This new type of probability theory is a function to the set of all subsets of the interval [0, 1] instead of to the interval [0, 1] itself, and hence its evaluation happens by means of a subset instead of a number. This subset corresponds to the different limits of sequences of relative frequency that can arise when an intrinsic lack of knowledge about the context and how it influences the state of the physical entity under study in the process of experimentation is taken into account. The new probability theory makes it possible to define probability on the whole set of experiments within the Geneva-Brussels approach to quantum mechanics, which was not possible with standard probability theory. We introduce the formal mathematical structure of a 'state experiment probability system', by using this new type of probability theory, as a general description of a physical entity by means of its states, experiments and probability. We derive the state property system as a special case of this structure, when we only consider the 'certain' aspects of the world. The categorySEPof state experiment probability systems and their morphisms is linked with the categorySPof state property systems and their morphisms, that has been studied in earlier articles in detail.- Aerts, D., Broekaert, J. and Gabora, L. (2002). Intrinsic contextuality as the crux of consciousness. In K. Yasue, M. Jibu and T. Della Senta (Eds.),
No Matter, Never Mind(pp. 173-181). Amsterdam: John Benjamins (Volume 33 of the seriesAdvances in Consciousness Research, ISSN 1381 -589X).- Aerts, D., Colebunders, E., Van der Voorde, A. and Van Steirteghem, B. (2002). On the amnestic modification of the category of state property systems.
Applied Categorical Structures,10, pp. 469-480.- Aerts, D., Czachor, M. and Durt, T. (Eds.) (2002).
Probing the Structure of Quantum Mechanics: Nonlinearity, Nonlocality, Probability and Axiomatics. Singapore: World Scientific.- Aerts, D., Czachor, M. and Durt, T. (2002). Probing the structure of quantum mechanics. In D. Aerts, M. Czachor and T. Durt (Eds.),
Probing the Structure of Quantum Mechanics: Nonlinearity, Nonlocality, Probability and Axiomatics(pp. 1-19). Singapore: World Scientific.- Aerts, D. and Deses, D. (2002). State property systems and closure spaces: extracting the classical and nonclassical parts. In D. Aerts, M. Czachor and T. Durt (Eds.),
Probing the Structure of Quantum Mechanics: Nonlinearity, Nonlocality, Probability and Axiomatics(pp. 130-148). Singapore: World Scientific. Archive reference and link: http://uk.arxiv.org/pdf/quant-ph/0404070.

Abstract:In earlier work an equivalence of the categories of state property systems and their morphisms and closure spaces and continuous maps was proven. It has been shown, using the equivalence between these two categories, that some of the axioms of quantum axiomatics are equivalent with separation axioms on the corresponding closure space. More particularly it was proven that the axiom of atomicity is equivalent to the T1 separation axiom. In the present article we analyze the intimate relation that exists between classical and nonclassical in the state property systems and disconnected and connected in the corresponding closure space. We introduce classical properties using the concept of super selection rule,i.e.two properties are separated by a superselection rule iff there do not exist 'superposition states' related to these two properties. Then we show that the classical properties of a state property system correspond exactly to the clopen subsets of the corresponding closure space. Thus connected closure spaces correspond precisely to state property systems for which the elements 0 and I are the only classical properties, the so called pure nonclassical state property systems. The main result is a decomposition theorem, which allows us to split a state property system into a number of 'pure nonclassical state property systems' and a 'totally classical state property system'. This decomposition theorem for a state property system is the translation of a decomposition theorem for the corresponding closure space into its connected components.- Aerts, D. and D'Hooghe B. (2002). Quantum computation: Towards the construction of a 'between quantum and classical computer'. In D. Aerts, M. Czachor and T. Durt (Eds.),
Probing the Structure of Quantum Mechanics: Nonlinearity, Nonlocality, Probability and Axiomatics(pp. 230-247). Singapore: World Scientific.

Abstract:Using the 'between quantum and classical' models that have been constructed explicitly within the hidden measurement approach of quantum mechanics we investigate the possibility to construct a 'between quantum and classical' computer. In this view, the pure quantum computer and the classical Turing machine can be seen as two special cases of our general computer. We have shown in earlier research that the intermediate 'between quantum and classical' systems cannot be described within standard quantum theory. We argue that the general categoral approach of state property systems might provide a unified framework for the study of these 'between quantum and classical' models, and hence also for the study of classical and quantum computers as special cases.- Aerts, D. and Valckenborgh, F. (2002). The linearity of quantum mechanics at stake: the description of separated quantum entities. In D. Aerts, M. Czachor and T. Durt (Eds.),
Probing the Structure of Quantum Mechanics: Nonlinearity, Nonlocality, Probability and Axiomatics(pp. 20-46). Singapore: World Scientific. Archive reference and link: http://uk.arxiv.org/abs/quant-ph/0205161.

Abstract:We concentrate on the situation of a physical entity that is the compound entity of two 'separated' quantum entities. In earlier work it has been proved by one of the authors that such a physical entity cannot be described by standard quantum mechanics. More specifically, it was shown that two of the axioms of traditional quantum axiomatics are at the origin of the impossibility for standard quantum mechanics to describe the compound entity of two separated quantum entities. One of these axioms is equivalent with the superposition principle, which means that separated quantum entities put the linearity of quantum mechanics at stake. We analyze the conceptual steps that are involved in this proof, and expose the necessary material of quantum axiomatics to be able to understand the argument.- Aerts, D. and Valckenborgh, F. (2002). Linearity and compound physical systems: the case of two separated spin 1/2 entities. In D. Aerts, M. Czachor and T. Durt (Eds.),
Probing the Structure of Quantum Mechanics: Nonlinearity, Nonlocality, Probability and Axiomatics(pp. 47-70). Singapore: World Scientific. Archive reference and link: http://uk.arxiv.org/abs/quant-ph/0205166.

Abstract:We illustrate some problems that are related to the existence of an underlying linear structure at the level of the property lattice associated with a physical system, for the particular case of two explicitly separated spin 1/2 objects that are considered, and mathematically described, as one compound system. It is shown that Aerts' separated product of the property lattices corresponding with the two spin 1/2 objects does not have an underlying linear structure, although the property lattices associated with the subobjects in isolation manifestly do. This is related at a fundamental level with the fact that separated products do not behave well with respect to the covering law of elementary lattice theory. In addition, we discuss the orthogonality relation associated with the separated product in general and consider the related problem of the behaviour of the corresponding Sasaki projections.- Gabora, L. and Aerts, D. (2002). Contextualizing concepts. In
Proceedings of the 15th International FLAIRS Conference (Special Track 'Categorization and Concept Representation: Models and Implications'), Pensacola Florida, May 14-17, 2002, American Association for Artificial Intelligence.

Abstract: The mathematics of quantum mechanics was developed to cope with problems arising in the description of (1) contextual interactions, and (2) the generation of new states with new properties when particles become entangled. Similar problems arise with concepts. This paper summarizes the rationale for and preliminary results of using a generalization of standard quantum mechanics based on the lattice formalism to describe the contextual manner in which concepts are evoked, used, and combined to generate meaning. Concepts are viewed not as fixed representations but dynamically Ôre-constructedÕ entities generated on the fly through interaction between cognitive state and situation or context.- Gabora, L. and Aerts, D. (2002). Contextualizing concepts using a mathematical generalization of the quantum formalism.
Journal of Experimental and Theoretical Artificial Intelligence,14, pp. 327-358. Archive reference and link: http://uk.arxiv.org/abs/quant-ph/0205161.

Abstract: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 here. Concepts are viewed not as fixed representations, but entities existing in states of potentiality that require interaction with a context---a stimulus or another concept---to `collapse' to observable form as an exemplar, prototype, or other (possibly imaginary) instance. The stimulus situation plays the role of the measurement in physics, acting as context that induces a change of the cognitive state from superposition state to collapsed state. The collapsed state is more likely to consist of a conjunction of concepts for associative than analytic thought because more stimulus or concept properties take part in the collapse. We provide two contextual measures of conceptual distance---one using collapse probabilities and the other weighted properties---and show how they can be applied to conjunctions using the pet fish problem.

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