Fuzzy Generalised Quantifiers for Natural Language in Categorical Compositional Distributional Semantics
This work addresses a computational bottleneck in natural language processing for researchers in compositional semantics, though it is incremental as it builds on existing fuzzy and distributional methods.
The paper tackled the computational cost of using powerset constructions in compositional distributional models for natural language quantifiers by introducing fuzzy quantifiers based on Zadeh's approach within many-valued relations, resulting in equivalent semantics without the need for powersets.
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.