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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 78 (40 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.
A theory of concepts and their combinations I: the structure of the sets of contexts and properties
, 2005
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Toward an ecological theory of concepts
 In (D. Aerts, B. D'Hooghe & N. Note, Eds.) Worldviews, Science and Us: Bridging Knowledge and Perspectives on the World, World Scientific
, 2005
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Spin as primordial selfreferential process driving quantum mechanics, spacetime dynamics and consciousness
 COGPRINTS ID3544 (2003); NEUROQUANTOLOGY
, 2004
"... We have recently theorized that consciousness is intrinsically connected to quantum mechanical spin since said spin is embedded in the microscopic structure of spacetime and is more fundamental than spacetime itself, that is, spin is the “mindpixel.” Applying these ideas to the particular structure ..."
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Cited by 27 (22 self)
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We have recently theorized that consciousness is intrinsically connected to quantum mechanical spin since said spin is embedded in the microscopic structure of spacetime and is more fundamental than spacetime itself, that is, spin is the “mindpixel.” Applying these ideas to the particular structures and dynamics of the brain, we have developed a qualitative model of quantum consciousness. In this paper, we express our fundamental view that spin is a primordial selfreferential process driving quantum mechanics, spacetime dynamics and consciousness. To justify such a view, we will draw support from existing literatures, discuss from a reductionist perspective the essential properties said spin should possess as mindpixel and explore further the nature of spin to see whether said properties are present. Our conclusion is that these properties are indeed endowed to spin by Nature. One of the implications from our fundamental view is that the probabilistic structure of quantum mechanics is due to the selfreferential collapse of spin state that is contextual, nonlocal, noncomputable and irreversible. Therefore, a complete theory of the selfreferential spin process is necessarily semantic, that is, it should be based on internally meaningful information.
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 21 (19 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
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 14 (11 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.