Dual Density Operators and Natural Language Meaning

TL;DR

This paper introduces dual density operators to represent both ambiguity and lexical entailment in natural language, enhancing compositional distributional semantics with a quantum-inspired framework.

Contribution

It proposes dual density operators for modeling two independent aspects of meaning, extending the use of density operators in natural language semantics.

Findings

Dual density operators can represent ambiguity and entailment simultaneously.

Demonstrated a proof-of-concept example in natural language semantics.

Extended quantum-inspired models to handle complex language phenomena.

Abstract

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.