The Frobenius anatomy of word meanings I: subject and object relative pronouns

TL;DR

This paper introduces a novel compositional vector-based semantic model for subject and object relative pronouns using Frobenius algebras within a categorical framework, integrating truth-theoretic and corpus-based approaches.

Contribution

It formalizes the semantics of relative pronouns with Frobenius algebras, enabling information passing and manipulation in a compositional vector space model.

Findings

Two instantiations: truth-theoretic and corpus statistics

Formal semantics for relative pronouns using Frobenius algebras

Enhanced modeling of relative clause semantics

Abstract

This paper develops a compositional vector-based semantics of subject and object relative pronouns within a categorical framework. Frobenius algebras are used to formalise the operations required to model the semantics of relative pronouns, including passing information between the relative clause and the modified noun phrase, as well as copying, combining, and discarding parts of the relative clause. We develop two instantiations of the abstract semantics, one based on a truth-theoretic approach and one based on corpus statistics.