Computational Semantics for Comparatives based on CCG and Theorem Proving

Abstract

Comparative constructions pose a challenge to Natural Language Inference (NLI), a task of determining whether a text entails a hypothesis. Comparatives are structurally complex in that they interact with other syntactic and semantic phenomena such as ellipsis, numerals, and lexical antonyms. In the context of Formal Semantics, there is a rich body of work on the compositional semantics of comparatives and other gradable expressions on the basis of the notion of degree. However, a computational inference system for comparatives is not developed enough to be used for NLI tasks. In this paper, we present a compositional semantics that maps various comparative constructions in English to semantic representations using current state-of-the-art Combinatory Categorial Grammar (CCG) parsers and introduces an inference system using automated theorem proving which effectively computes complex logical inference with comparatives. We evaluate our system on three NLI datasets that contain complex inferences with comparatives, quantifiers, and numerals. We show that the system achieves better performance, in comparison with recent logic-based and deep-learning-based NLI systems.