Towards Modeling Natural Language Inferences with Part-Whole Relations using Formal Ontology and Lexical Semantics

In this paper, we present a framework of natural language semantics combined with formal ontology to deal with lexical and world knowledge. We build on a framework of Dependent Type Semantics (DTS), a framework of natural language semantics based on dependent type theory. We show how to handle natural language inferences with part-whole relations, in particular, bridging inferences and inferences with the socalled total and partial predicates, in this framework. Introduction Entailment relations are of central importance in the study of formal semantics for natural languages. Generally speaking, the task of determining whether one sentence intuitively entails another sentence requires vast amounts of lexical and world knowledge. Over the past several decades, however, formal semanticists have concentrated on a relatively small set of entailment relations that arise from the compositional structure of a sentence, and in doing so, have abstracted away from how logical inferences interact with a rich body of lexical and world knowledge. Meanwhile, since the emergence of statistical parsers based on sophisticated syntactic theories (Clark and Curran 2007), there has been developed a wide-coverage semantic parser that translates sentences into logical formulas and recognizes entailments using theorem proving (Bos 2008). Then it has been of increasing importance to combine well-developed methods of formal semantics with a rich body of lexical and world knowledge for natural language inferences. For that purpose, large lexical resources such as WordNet (Fellbaum 1998) have been widely used, and there have been attempts to improve the quality of such resources using the concepts of formal ontology (Gangemi et al. 2003). At present, however, there are few attempts to combine such an ontology with the state-of-the-art formal semantics; moreover, there is little discussion on what kind of knowledge is needed to represent a variety of inferences in natural languages from a linguistic point of view. In this paper, we propose a framework of natural language semantics combined with formal ontology to deal with lexical and world knowledge. We build on a framework of DeCopyright c ⃝ 2015 for this paper by its authors. Copying permitted for private and academic purposes. pendent Type Semantics (DTS), a framework of natural language semantics based on dependent type theory (MartinLöf 1984). A special attention will be paid to the inferences that are sensitive to the part-whole relations among structured entities, in particular, bridging inferences and inferences with total and partial predicates. Formal semantics has been developed as sentence semantics and then further extended to discourse semantics in 1980’s. However, the attempt to combine formal semantics with lexical semantics is still underdeveloped. The present paper also aims to contribute to filling this gap, by means of enriching type-theoretical semantics of DTS with a mechanism to handle inferences based on lexical knowledge. Textual entailment and formal ontology To recognize an entailment relation between sentences requires one to grasp a piece of world knowledge that is not explicitly delivered in given premises. To formally capture the relevant knowledge, we focus on two types of semantic links between concepts: is-a links and part-of links. The so-called monotonicity inference (Icard and Moss 2014) is a typical instance of inferences that require knowledge expressed by is-a links. For example, to derive an inference A Eurostar runs ⇒ A train runs, we need to rely on the knowledge that a Eurostar is a train. Part-of links are used to describe parthood relations between concepts. An important class of inferences that depend on part-of links is bridging inference (Clark 1975): (1) John got on a Eurostar and wanted to eat dinner. But the buffet car was not open. To establish an anaphoric relation between the underlined noun phrases, one needs to use the knowledge that a buffet car is part of a Eurostar. What plays a crucial role in deriving such a bridging inference is role concept (Mizoguchi 2004). In contrast to basic concepts such as train and human, concepts like buffet car, brake and passenger represent a role in the context determined by the concept train. In general, a bridging inference is triggered by the expression denoting a role concept in a semantic representation; then the antecedent of the anaphora is identified with the concept that provides a context for the role concept. We will provide a formal representation of bridging inferences below. To derive entailment relations and resolve anaphoric dependencies, one needs to give a formal description of world knowledge and then combine it with semantic representations (SRs) for the premises and conclusion. In this paper, we use a framework of DTS for building semantic representations. The entire system of building semantic representations and deriving entailment relations is pictured in Fig. 1.