Fuzzy Generalised Quantifiers for Natural Language in Categorical Compositional Distributional Semantics

TL;DR

This paper introduces a fuzzy approach to generalized quantifiers in natural language semantics, avoiding computationally expensive powerset constructions by using many-valued relations, aligning with Zadeh's fuzzy quantifiers.

Contribution

It presents a novel fuzzy categorical model for generalized quantifiers that simplifies computation while maintaining semantic equivalence with Zadeh's fuzzy quantifiers.

Findings

Fuzzy categorical model matches Zadeh's fuzzy quantifier semantics

Avoids powerset construction in compositional distributional semantics

Enables more efficient fuzzy quantification in natural language processing

Abstract

Recent work on compositional distributional models shows that bialgebras over finite dimensional vector spaces can be applied to treat generalised quantifiers for natural language. That technique requires one to construct the vector space over powersets, and therefore is computationally costly. In this paper, we overcome this problem by considering fuzzy versions of quantifiers along the lines of Zadeh, within the category of many valued relations. We show that this category is a concrete instantiation of the compositional distributional model. We show that the semantics obtained in this model is equivalent to the semantics of the fuzzy quantifiers of Zadeh. As a result, we are now able to treat fuzzy quantification without requiring a powerset construction.