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120
Foundations of Quantum Physics: a General Realistic and
 Operational Approach, Int. J. Theor. Phys
, 1999
"... We present a general formalism with the aim of describing the situation of an entity, how it is, how it reacts to experiments, how we can make statistics with it, and how it ‘changes ’ under the influence of the rest of the universe. Therefore we base our formalism on the following basic notions: (1 ..."
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Cited by 35 (25 self)
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We present a general formalism with the aim of describing the situation of an entity, how it is, how it reacts to experiments, how we can make statistics with it, and how it ‘changes ’ under the influence of the rest of the universe. Therefore we base our formalism on the following basic notions: (1) the states of the entity; they describe the modes of being of the entity, (2) the experiments that can be performed on the entity; they describe how we act upon and collect knowledge about the entity, (3) the probabilities; they describe our repeated experiments and the statistics of these repeated experiments, (4) the symmetries; they describe the interactions of the entity with the external world without being experimented upon. Starting from these basic notions we formulate the necessary derived notions: mixed states, mixed experiments and events, an eigen closure structure describing the properties of the entity, an ortho closure structure introducing an orthocomplementation, outcome determination, experiment determination, state determination and atomicity giving rise to some of the topological separation axioms for the closures. We define the notion of sub entity in a general way and identify the morphisms of our structure. We study specific examples in detail in the light of this formalism: a classical deterministic entity and a quantum entity described by the standard quantum mechanical formalism. We present a possible solution to the problem of the description of sub entities within the standard quantum mechanical procedure using the tensor product of the Hilbert spaces, by introducing a new completed quantum mechanics in Hilbert space, were new ‘pure ’ states are introduced, not represented by rays of the Hilbert space.
Contextualizing concepts using a mathematical generalization of the quantum formalism
 Trends in Cognitive Science
, 2000
"... 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 deve ..."
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Cited by 28 (18 self)
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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 an instantiated form (e.g. 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.
Steirteghem, State property systems and closure spaces: a study of categorical equivalence
 International Journal of Theoretical Physics
, 1999
"... In [1] an equivalence of the categories SP and Cls was proven. The category SP consists of the state property systems [2] and their morphisms, which are the mathematical structures that describe a physical entity by means of its states and properties [3, 4, 5, 6, 7, 8]. The category Cls consists of ..."
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Cited by 27 (25 self)
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In [1] an equivalence of the categories SP and Cls was proven. The category SP consists of the state property systems [2] and their morphisms, which are the mathematical structures that describe a physical entity by means of its states and properties [3, 4, 5, 6, 7, 8]. The category Cls consists of the closure spaces and the continuous maps. In earlier work it has been shown, using the equivalence between Cls and SP, 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 [9]. 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, elaborating results that appeared in [10, 11]. 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
A Partial Order on Classical and Quantum States
, 2002
"... We introduce a partial order on classical and quantum states which reveals that these sets are actually domains: Directed complete partially ordered sets with an intrinsic notion of approximation. The operational significance of the orders involved conclusively establishes that physical information ..."
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Cited by 19 (6 self)
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We introduce a partial order on classical and quantum states which reveals that these sets are actually domains: Directed complete partially ordered sets with an intrinsic notion of approximation. The operational significance of the orders involved conclusively establishes that physical information has a natural domain theoretic structure. In the same
Physical traces: Quantum vs. classical information processing
 In Proceedings of Category Theory and Computer Science 2002 (CTCS’02), volume 69 of Electronic Notes in Theoretical Computer Science. Elsevier Science
, 2003
"... a setting that enables qualitative differences between classical and quantum processes to be explored. The key construction is the physical interpretation/realization of the traced monoidal categories of finitedimensional vector spaces with tensor product as monoidal structure and of finite sets an ..."
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Cited by 17 (5 self)
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a setting that enables qualitative differences between classical and quantum processes to be explored. The key construction is the physical interpretation/realization of the traced monoidal categories of finitedimensional vector spaces with tensor product as monoidal structure and of finite sets and relations with Cartesian product as monoidal structure, both of them providing a socalled wavestyle GoI. The developments in this paper reveal that envisioning state update due to quantum measurement as a process provides a powerful tool for developing highlevel approaches to quantum information processing.
Quantaloids describing causation and propagation for physical properties
 Foundations of Physics Letters
, 2001
"... We study some particular examples of quantaloids and corresponding morphisms, originating from primitive physical reasonings on the lattices of properties of physical systems. ..."
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Cited by 17 (9 self)
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We study some particular examples of quantaloids and corresponding morphisms, originating from primitive physical reasonings on the lattices of properties of physical systems.
Quantum mechanics: structures, axioms and paradoxes
 in Quantum Mechanics and the Nature of Reality
, 1999
"... We present an analysis of quantum mechanics and its problems and paradoxes taking into account the results that have been obtained during the last two decades by investigations in the field of ‘quantum structures research’. We concentrate mostly on the results of our group FUND at Brussels Free Univ ..."
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Cited by 14 (9 self)
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We present an analysis of quantum mechanics and its problems and paradoxes taking into account the results that have been obtained during the last two decades by investigations in the field of ‘quantum structures research’. We concentrate mostly on the results of our group FUND at Brussels Free University. By means of a spin 1 2 model where the quantum probability is generated by the presence of fluctuations on the interactions between measuring apparatus and physical system, we show that the quantum structure can find its origin in the presence of these fluctuations. This appraoch, that we have called the ‘hidden measurement approach’, makes it possible to construct systems that are in between quantum and classical. We show that two of the traditional axioms of quantum axiomatics are not satisfied for these ‘in between quantum and classical’ situations, and how this structural shortcoming of standard quantum mechanics is at the origin of most of the quantum paradoxes. We show that in this approach the EPR paradox identifies a genuine incompleteness of standard quantum mechanics, however not an incompleteness that means the lacking of hidden variables, but an incompleteness pointing at the impossibility for standard quantum mechanics to describe separated quantum systems. We indicate in which way, by redefining the meaning of density states, standard quantum mechanics can be completed. We put forward in which way the axiomatic approach to quantum mechanics can be compared to the traditional axiomatic approach to relativity theory, and how this might lead to studying another road to unification of both theories.
Being and change: foundations of a realistic operational formalism
 in Probing the Structure of Quantum Mechanics: Nonlinearity, Nonlocality, Probability and Axiomatics
, 2002
"... 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 have to be a physical entity, but can also be an entity of a more abstract nature, for example a concept, or a cultur ..."
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Cited by 14 (12 self)
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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 have 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. However, 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 categorical setting and derive the morphisms between
Operational Resolutions And State Transitions In A Categorical Setting
 Found. Phys. Letters
, 1998
"... this paper consists of lifting the  categorically  equivalent descriptions of physical systems by a (i) `state space' or a (ii) `property lattice'  see [14,20,25,26]  to an asymmetrical  i.e., not anymore isomorphic  duality on the level of: (i) ..."
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Cited by 13 (10 self)
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this paper consists of lifting the  categorically  equivalent descriptions of physical systems by a (i) `state space' or a (ii) `property lattice'  see [14,20,25,26]  to an asymmetrical  i.e., not anymore isomorphic  duality on the level of: (i)
Contextualizing Concepts
, 2002
"... 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 ..."
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Cited by 13 (10 self)
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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 `reconstructed' entities generated on the fly through interaction between cognitive state and situation or context.