Dual Density Operators and Natural Language Meaning

Daniela Ashoush
(Univesity of Oxford)
Bob Coecke
(Univesity of Oxford)

Density operators allow for representing ambiguity about a vector representation, both in quantum theory and in distributional natural language meaning. Formally equivalently, they allow for discarding part of the description of a composite system, where we consider the discarded part to be the context. We introduce dual density operators, which allow for two independent notions of context. We demonstrate the use of dual density operators within a grammatical-compositional distributional framework for natural language meaning. We show that dual density operators can be used to simultaneously represent: (i) ambiguity about word meanings (e.g. queen as a person vs. queen as a band), and (ii) lexical entailment (e.g. tiger -> mammal). We provide a proof-of-concept example.

In Dimitrios Kartsaklis, Martha Lewis and Laura Rimell: Proceedings of the 2016 Workshop on Semantic Spaces at the Intersection of NLP, Physics and Cognitive Science (SLPCS 2016), Glasgow, Scotland, 11th June 2016, Electronic Proceedings in Theoretical Computer Science 221, pp. 1–10.
Published: 2nd August 2016.

ArXived at: http://dx.doi.org/10.4204/EPTCS.221.1 bibtex PDF
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