A Theory of Concepts and Their Combinations II: A Hilbert Space Representation Export

@misc{citeulike:1145681, abstract = {The sets of contexts and properties of a concept are embedded in the complex Hilbert space of quantum mechanics. States are unit vectors or density operators, and contexts and properties are orthogonal projections. The way calculations are done in Hilbert space makes it possible to model how context influences the state of a concept. Moreover, a solution to the combination of concepts is proposed. Using the tensor product, a procedure for describing combined concepts is elaborated, providing a natural solution to the pet fish problem. This procedure allows the modeling of an arbitrary number of combined concepts. By way of example, a model for a simple sentence containing a subject, a predicate and an object, is presented.}, archivePrefix = {arXiv}, author = {Aerts, Diederik and Gabora, Liane}, citeulike-article-id = {1145681}, citeulike-linkout-0 = {http://arxiv.org/abs/quant-ph/0402205}, citeulike-linkout-1 = {http://arxiv.org/pdf/quant-ph/0402205}, day = {26}, eprint = {quant-ph/0402205}, keywords = {category, concept, context, fish, hilbert, mechanics, memory, problem, product, property, prototype, quantum, space, state, structure, tensor}, month = {Feb}, posted-at = {2008-01-16 01:24:17}, priority = {2}, title = {A Theory of Concepts and Their Combinations II: A Hilbert Space Representation}, url = {http://arxiv.org/abs/quant-ph/0402205}, year = {2004} }

TY - ELEC ID - citeulike:1145681 L3 - citeulike-article-id:1145681 N2 - The sets of contexts and properties of a concept are embedded in the complex Hilbert space of quantum mechanics. States are unit vectors or density operators, and contexts and properties are orthogonal projections. The way calculations are done in Hilbert space makes it possible to model how context influences the state of a concept. Moreover, a solution to the combination of concepts is proposed. Using the tensor product, a procedure for describing combined concepts is elaborated, providing a natural solution to the pet fish problem. This procedure allows the modeling of an arbitrary number of combined concepts. By way of example, a model for a simple sentence containing a subject, a predicate and an object, is presented. TI - A Theory of Concepts and Their Combinations II: A Hilbert Space Representation KW - category KW - concept KW - context KW - fish KW - hilbert KW - mechanics KW - memory KW - problem KW - product KW - property KW - prototype KW - quantum KW - space KW - state KW - structure KW - tensor AU - Aerts, Diederik AU - Gabora, Liane PY - 2004/Feb/26/ UR - http://arxiv.org/abs/quant-ph/0402205 ER -