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Comparative constructions play an important role in natural language inference. However, attempts to study semantic representations and logical inferences for comparatives from the computational perspective are not well developed, due to the complexity of their syntactic structures and inference patterns. In this study, using a framework based on Combinatory Categorial Grammar (CCG), we present a compositional semantics that maps various comparative constructions in English to semantic representations and introduces an inference system that effectively handles logical inference with comparatives, including those involving numeral adjectives, antonyms, and quantification. We evaluate the performance of our system on the FraCaS test suite and show that the system can handle a variety of complex logical inferences with comparatives.
In formal semantics, there are two well-developed semantic frameworks: event semantics, which treats verbs and adverbial modifiers using the notion of event, and degree semantics, which analyzes adjectives and comparatives using the notion of degree.
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