Categorical Vector Space Semantics for Lambek Calculus with a Relevant Modality (Extended Abstract)

TL;DR

This paper introduces a novel categorical vector space semantics for Lambek Calculus with a Relevant Modality, enabling semantic modeling of complex linguistic phenomena like parasitic gaps and evaluating their effectiveness with modern NLP embeddings.

Contribution

It develops a new categorical compositional semantics framework for Lambek Calculus with a Relevant Modality, integrating vector space models and applying it to parasitic gap interpretation.

Findings

Effective disambiguation of parasitic gap phrases using the proposed model.

Successful instantiation of the categorical semantics in finite-dimensional vector spaces.

Demonstrated compatibility with BERT, Word2Vec, and FastText embeddings.

Abstract

We develop a categorical compositional distributional semantics for Lambek Calculus with a Relevant Modality, which has a limited version of the contraction and permutation rules. The categorical part of the semantics is a monoidal biclosed category with a coalgebra modality as defined on Differential Categories. We instantiate this category to finite dimensional vector spaces and linear maps via quantisation functors and work with three concrete interpretations of the coalgebra modality. We apply the model to construct categorical and concrete semantic interpretations for the motivating example of this extended calculus: the derivation of a phrase with a parasitic gap. The effectiveness of the concrete interpretations are evaluated via a disambiguation task, on an extension of a sentence disambiguation dataset to parasitic gap phrases, using BERT, Word2Vec, and FastText vectors and Relational tensors