Dual Density Operators and Natural Language Meaning

• Main Authors: Daniela Ashoush, Bob Coecke
• Format: Article
• Language: English
• Published: Open Publishing Association 2016-08-01
• Series: Electronic Proceedings in Theoretical Computer Science
• Online Access: http://arxiv.org/pdf/1608.01401v1

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.