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

arXiv eprints
 Pub Date:
 February 2004
 arXiv:
 arXiv:quantph/0402205
 Bibcode:
 2004quant.ph..2205A
 Keywords:

 Quantum Physics
 EPrint:
 21 pages, to appear in the journal 'Kybernetes' in the Summer of 2004