arXiv:quant-ph/0402205quant-ph
A Theory of Concepts and Their Combinations II: A Hilbert Space Representation
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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.
One of the main references, and other interesting stuff can be found on Bob Coecke's site: http://www.comlab.ox.ac.uk/bob.coecke/ Personally, I think the NLP problem is, and will always be, a graph problem. To the extent that you can approximate and accelerate graph algorithms…
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