Linguists Who Use Probabilistic Models Love Them: Quantification in Functional Distributional Semantics

Abstract: Functional Distributional Semantics provides a computationally tractable framework for learning truth-conditional semantics from a corpus. Previous work in this framework has provided a probabilistic version of first-order logic, recasting quantification as Bayesian inference. In this paper, I show how the previous formulation gives trivial truth values when a precise quantifier is used with vague predicates. I propose an improved account, avoiding this problem by treating a vague predicate as a distribution over precise predicates. I connect this account to recent work in the Rational Speech Acts framework on modelling generic quantification, and I extend this to modelling donkey sentences. Finally, I explain how the generic quantifier can be both pragmatically complex and yet computationally simpler than precise quantifiers.