On the Proper Treatment of Quantifiers in Probabilistic Logic Semantics

As a format for describing the meaning of natural language sentences, probabilistic logic combines the expressivity of first-order logic with the ability to handle graded information in a principled fashion. But practical probabilistic logic frameworks usually assume a finite domain in which each entity corresponds to a constant in the logic (domain closure assumption). They also assume a closed world where everything has a very low prior probability. These assumptions lead to some problems in the inferences that these systems make. In this paper, we show how to formulate Textual Entailment (RTE) inference problems in probabilistic logic in a way that takes the domain closure and closed-world assumptions into account. We evaluate our proposed technique on three RTE datasets, on a synthetic dataset with a focus on complex forms of quantification, on FraCas and on one more natural dataset. We show that our technique leads to improvements on the more natural dataset, and achieves 100% accuracy on the synthetic dataset and on the relevant part of FraCas.