A Theory of Concepts and Their Combinations I: The Structure of the Sets of Contexts and Properties Export

@misc{citeulike:1145675, abstract = {We propose a theory for modeling concepts that uses the state-context-property theory (SCOP), a generalization of the quantum formalism, whose basic notions are states, contexts and properties. This theory enables us to incorporate context into the mathematical structure used to describe a concept, and thereby model how context influences the typicality of a single exemplar and the applicability of a single property of a concept. We introduce the notion `state of a concept' to account for this contextual influence, and show that the structure of the set of contexts and of the set of properties of a concept is a complete orthocomplemented lattice. The structural study in this article is a preparation for a numerical mathematical theory of concepts in the Hilbert space of quantum mechanics that allows the description of the combination of concepts (see <a href="/abs/quant-ph/0402205">quant-ph/0402205</a>)}, archivePrefix = {arXiv}, author = {Aerts, Diederik and Gabora, Liane}, citeulike-article-id = {1145675}, citeulike-linkout-0 = {http://arxiv.org/abs/quant-ph/0402207}, citeulike-linkout-1 = {http://arxiv.org/pdf/quant-ph/0402207}, day = {26}, eprint = {quant-ph/0402207}, keywords = {all-logical-theories, chu-space, closure, closure-structures, concept-lattice, conceptual-structures, domain-theory, fca, iff, inference, information-system, logical-information-system, logical-structures}, month = {Feb}, posted-at = {2007-03-07 14:11:43}, priority = {2}, title = {A Theory of Concepts and Their Combinations I: The Structure of the Sets of Contexts and Properties}, url = {http://arxiv.org/abs/quant-ph/0402207}, year = {2004} }

TY - ELEC ID - citeulike:1145675 L3 - citeulike-article-id:1145675 N2 - We propose a theory for modeling concepts that uses the state-context-property theory (SCOP), a generalization of the quantum formalism, whose basic notions are states, contexts and properties. This theory enables us to incorporate context into the mathematical structure used to describe a concept, and thereby model how context influences the typicality of a single exemplar and the applicability of a single property of a concept. We introduce the notion `state of a concept' to account for this contextual influence, and show that the structure of the set of contexts and of the set of properties of a concept is a complete orthocomplemented lattice. The structural study in this article is a preparation for a numerical mathematical theory of concepts in the Hilbert space of quantum mechanics that allows the description of the combination of concepts (see <a href="/abs/quant-ph/0402205">quant-ph/0402205</a>) TI - A Theory of Concepts and Their Combinations I: The Structure of the Sets of Contexts and Properties KW - all-logical-theories KW - chu-space KW - closure KW - closure-structures KW - concept-lattice KW - conceptual-structures KW - domain-theory KW - fca KW - iff KW - inference KW - information-system KW - logical-information-system KW - logical-structures AU - Aerts, Diederik AU - Gabora, Liane PY - 2004/Feb/26/ UR - http://arxiv.org/abs/quant-ph/0402207 ER -