Combining Event Semantics and Degree Semantics for Natural Language Inference (2020)

Abstract: 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. However, it is not obvious whether these frameworks can be combined to handle cases in which the phenomena in question are interacting with each other. Here, we study this issue by focusing on natural language inference (NLI). We implement a logic-based NLI system that combines event semantics and degree semantics and their interaction with lexical knowledge. We evaluate the system on various NLI datasets containing linguistically challenging problems. The results show that the system achieves high accuracies on these datasets in comparison with previous logic-based systems and deep-learning-based systems. This suggests that the two semantic frameworks can be combined consistently to handle various combinations of linguistic phenomena without compromising the advantage of either framework.

## introduction since @xcite , formal compositional semantics has provided successful accounts of linguistic phenomena using logical expressions along with syntactic structures. in recent years, with the development of wide-coverage parsers such as combinatory categorial grammar (ccg) parsers @xcite , some of the formal theories have been implemented as robust computational semantics @xcite @xcite and have been applied to natural language inference (nli), which is the task of determining whether a text entails a hypothesis. this paper attempts to push forward this paradigm by focusing on the interaction of two semantic frameworks, namely, event semantics and degree semantics. generally speaking, research in linguistic formal semantics has tended to focus on creating an indepth theory for a variety of linguistic phenomena, such as quantifiers, adjectives, comparatives, and tense. however, it is often not obvious whether these independent theories can be combined and extended to cases in which the phenomena in question interact. thus, event semantics has been developed largely to account for the semantics of verb phrases and adverbial modifiers @xcite . in contrast, degree semantics provides an analysis of gradable expressions such as adjectives and comparatives, using the notion of degree @xcite @xcite . although each theory has been elaborated for its own sake, it is not clear how to combine these two and handle expressions that require the application of both theories, such as the comparative form of adverbs, though it is a necessary step for analyzing real texts. the computational modeling of compositional semantic theories mentioned above enables us to precisely compute the predictions of each theory. in addition, their application to nli tasks provides a systematic way of evaluating a formal semantic theory. building on the previous logic-based approaches to nli, we present a logic-based nli system that combines event semantics and degree semantics, and more specifically, we build on the system presented in @xcite , which implements degree semantics for comparatives and generalized quantifiers. the system is limited, however, in that it does not implement event semantics, and hence does not handle inferences with adverbs and related constructions. also, it only covers a small portion of the generalized quantifiers discussed in the linguistics literature and does not handle inferences requiring lexical knowledge, thus being confined to purely logical inferences. to test the compatibility of event semantics and degree semantics, we add a layer of event semantics and lexical knowledge to that system and attempt to broaden its empirical coverage consistently. to evaluate the system, we assess its capacity to handle (i) a set of logical compositional inferences and (ii) their interaction with lexical knowledge. for (i), we use fracas @xcite , which contains various semantically complex inferences and cad @xcite , which contains complex inferences with adjectives and comparatives. to our knowledge, there is no linguistically controlled dataset that contains inferences with adverbs, so we create a set of logical inferences with adverbs and related constructions and use it to evaluate the system. for (ii), we use med @xcite , which contains problems with monotonicity inferences and lexical knowledge, and sick @xcite , which focuses on lexical inferences combined with linguistic phenomena such as negation and quantifiers. in addition, we use hans @xcite , which is designed to probe the capacity of nli models based on deep learning (dl) and contains structural inferences, including those concerning adjectives and adverbs. the results show that our system achieves high accuracies across various datasets, supporting our claim that event semantics and degree semantics can be effectively combined for nli. ## system architecture for the implementation of an nli system foot_0 , we follow the basic architecture of @xcite . input sentences (i.e., a set of premises p 1 , . . . , p n and a hypothesis h) are mapped to ccg derivation trees using off-the-shelf ccg parsers. to accommodate output derivation trees in formal semantic analysis, various tree transformations are applied. then, using a set of semantic templates that assign lambdaexpressions to ccg categories @xcite , the output trees are mapped to logical forms, which are formulas of first-order logic (fol) with equality and arithmetic operations. this provides a set of formulas p 1 , . . . , p n for the premises and h for the hypothesis. then, an fol theorem prover tries to prove p 1 ∧ • • • ∧ p @xmath0. if it is successful, the system outputs yes (entailment). otherwise, the system tries to prove p 1 ∧ • • • ∧ p @xmath1. if both attempts fail, the system outputs unknown (neutral). for our purposes, we add two components to this basic architecture: (i) we extend the set of the semantic template to accommodate event semantics and various types of generalized quantifiers, and (ii) we add a mechanism to insert lexical knowledge before theorem proving. combining event semantics and degree semantics we use standard neo-davidsonian event semantics @xcite , which analyzes sentences as involving quantification over events. for instance, the sentence john ran is analyzed as ∃e(run(e) ∧ (subj(e) = john)), where subj is a function term that associates an event to its participant (subject). a sentence containing an adverb, for example, john ran slowly, is analyzed as ∃e(run(e) ∧ (subj(e) = john) ∧ slowly(e)), where the adverb slowly acts as a predicate of an event. this allows us to derive an inference from john ran slowly to john ran, that is, an inference to drop adverbial phrases. type example logical form upward many people cried. ∃x(people(x) ∧ many(x, θ many (person)) ∧ ∃e(cry(e) ∧ (subj(e) = x))) downward less than five students laughed. ¬∃x(student(x) ∧ many(x, 5) ∧ ∃e(laugh(e) ∧ (subj(e) = x))) non-monotone exactly eleven boys play soccer. ∃x(boy(x) ∧ many(x, 11) ∧ ∃e(play(e) ∧ (subj(e) = x) ∧ (obj(e) = soccer))) ∧∀x∀δ(boy(x) ∧ many(x, δ) ∧ ∃e(play(e) ∧ (subj(e) = x) ∧ (obj(e) = soccer)) → (δ < 12)) for degree semantics, we use the one presented in @xcite . it analyzes a gradable adjective tall as a binary predicate tall(x, δ) holding of an entity x and a degree δ @xcite . thus, the sentence chris is 5 feet tall is mapped to the logical form tall(chris, 5 feet). when a degree expression like 5 feet is absent, δ is set to a default value (for which we use a fixed constant); e.g., chris is tall is mapped to tall(chris, θ tall ). comparative expressions are analyzed in terms of first-order logic, using the so-called a-not-a analysis @xcite @xcite ; for example, chris is taller than alex is analyzed as ∃δ(tall(chris, δ) ∧ ¬tall(alex, δ)), which asserts that there is a degree δ of tallness that chris satisfies but alex does not. see @xcite for more detail. this analysis can be naturally extended to adverbial phrases and their comparative forms. ## conclusion we have presented a logic-based nli system that combines event semantics and degree semantics and evaluated the system on various datasets containing semantically challenging inferences. the results showed that the combination of event semantics and degree semantics is viable and works well on the type of complex logical inferences for which standard dl-based systems show poor performance. this study contributes to the study of computational modeling and the evaluation of formal semantic theories, as well as to the creation of challenging nli problems that dl-based models need to address.