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\nHilbert space of quantum mechanics. States are unit vectors or density\noperators, and contexts and properties are orthogonal projections. The way\ncalculations are done in Hilbert space makes it possible to model how context\ninfluences the state of a concept. Moreover, a solution to the combination of\nconcepts is proposed. Using the tensor product, a procedure for describing\ncombined concepts is elaborated, providing a natural solution to the pet fish\nproblem. This procedure allows the modeling of an arbitrary number of combined\nconcepts. By way of example, a model for a simple sentence containing a\nsubject, a predicate and an object, is presented.\n