Coordination in Categorical Compositional Distributional Semantics

TL;DR

This paper addresses the challenge of representing semantically vacuous words like coordinators in categorical compositional distributional semantics by leveraging Frobenius operators to model coordination across syntactic types.

Contribution

It introduces a novel morphism for coordinator tensors using Frobenius operators within a compact closed category framework, extending from atomic to compound types.

Findings

Provides a morphism for coordinator tensors

Demonstrates lifting from atomic to compound types

Discusses linguistic implications of Frobenius operators

Abstract

An open problem with categorical compositional distributional semantics is the representation of words that are considered semantically vacuous from a distributional perspective, such as determiners, prepositions, relative pronouns or coordinators. This paper deals with the topic of coordination between identical syntactic types, which accounts for the majority of coordination cases in language. By exploiting the compact closed structure of the underlying category and Frobenius operators canonically induced over the fixed basis of finite-dimensional vector spaces, we provide a morphism as representation of a coordinator tensor, and we show how it lifts from atomic types to compound types. Linguistic intuitions are provided, and the importance of the Frobenius operators as an addition to the compact closed setting with regard to language is discussed.