Dual Density Operators and Natural Language Meaning
This work addresses the challenge of modeling nuanced semantic relationships in natural language processing, though it appears incremental as it builds on existing density operator frameworks.
The paper tackles the problem of representing both ambiguity and lexical entailment in natural language meaning by introducing dual density operators, which allow for two independent notions of context, and demonstrates their use in a grammatical-compositional distributional framework with a proof-of-concept example.
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.