arXiv:quant-ph/0402207quant-ph
A Theory of Concepts and Their Combinations I: The Structure of the Sets of Contexts and Properties
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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 quant-ph/0402205)
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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