Anaphora and Ellipsis in Lambek Calculus with a Relevant Modality: Syntax and Semantics

TL;DR

This paper extends a Lambek calculus with a relevant modality to include anaphora and ellipsis, providing a compositional vector space semantics that captures ambiguous readings and disambiguates ellipsis in natural language.

Contribution

It develops a vector space semantics for Lambek calculus with a relevant modality, interpreting anaphora and ellipsis, and demonstrates its effectiveness in disambiguation tasks.

Findings

Successfully interprets anaphora and ellipsis in vector space models.

Derives sloppy and strict readings of ambiguous anaphora with ellipsis.

Experiments show improved disambiguation performance.

Abstract

Lambek calculus with a relevant modality $!\mathbf{L^*}$ of arXiv:1601.06303 syntactically resolves parasitic gaps in natural language. It resembles the Lambek calculus with anaphora $\mathbf{LA}$ of (J\"ager, 1998) and the Lambek calculus with controlled contraction, $\mathbf{L}_{\Diamond}$, of arXiv:1905.01647v1 which deal with anaphora and ellipsis. What all these calculi add to Lambek calculus is a copying and moving behaviour. Distributional semantics is a subfield of Natural Language Processing that uses vector space semantics for words via co-occurrence statistics in large corpora of data. Compositional vector space semantics for Lambek Calculi are obtained via the DisCoCat models arXiv:1003.4394v1. $\mathbf{LA}$ does not have a vector space semantics and the semantics of $\mathbf{L}_{\Diamond}$ is not compositional. Previously, we developed a DisCoCat semantics for $!\mathbf{L^*}$ and focused on the parasitic gap applications. In this paper, we use the vector space instance of that general semantics and show how one can also interpret anaphora, ellipsis, and for the first time derive the sloppy vs strict vector readings of ambiguous anaphora with ellipsis cases. The base of our semantics is tensor algebras and their finite dimensional variants: the Fermionic Fock spaces of Quantum Mechanics. We implement our model and experiment with the ellipsis disambiguation task of arXiv:1905.01647.