Higher-order logical inference with compositional semantics

Proceedings of the 2015 Conference on Empirical Methods in Natural Language Processing, pages 2055–2061, Lisbon, Portugal, 17-21 September 2015. c⃝2015 Association for Computational Linguistics. Higher-order logical inference with compositional semantics Koji Mineshima1,3 mineshima.koji@ocha.ac.jp Pascual Mart´ınez-G´omez1,2,3 pascual@nii.ac.jp Yusuke Miyao2 yusuke@nii.ac.jp Daisuke Bekki1,2,3 bekki@is.ocha.ac.jp 1Ochanomizu University Tokyo, Japan 2National Institute of Informatics Tokyo, Japan 3CREST, JST Saitama, Japan Abstract We present a higher-order inference sys- tem based on a formal compositional semantics and the wide-coverage CCG parser. We develop an improved method to bridge between the parser and seman- tic composition. The system is evaluated on the FraCaS test suite. In contrast to the widely held view that higher-order logic is unsuitable for efficient logical inferences, the results show that a system based on a reasonably-sized semantic lexicon and a manageable number of non-first-order ax- ioms enables efficient logical inferences, including those concerned with general- ized quantifiers and intensional operators, and outperforms the state-of-the-art first- order inference system. 1 Introduction Entailment relations are of central importance in the enterprise of both formal and computational semantics. Traditionally, formal semanticists have concentrated on a relatively small set of linguis- tic inferences. However, since the emergence of statistical parsers based on sophisticated syntac- tic theories (Clark and Curran, 2007), an open do- main system has been developed that supports cer- tain degree of robust semantic interpretation with wide coverage (Bos et al., 2004). It is then rea- sonable to expect that a state-of-the-art formal se- mantics provides an accurate computational basis of natural language inferences. However, there are still obstacles in the way of achieving this goal. One is that the statistical parsers on which semantic interpretations rely do not necessarily reflect the best syntactic analysis as assumed in the formal semantics literature (Honni- bal et al., 2010). Another persistent problem is the gap between the logics employed in the two com- munities; while it is generally assumed among for- mal semanticists that adequate semantic represen- tations for natural language demand higher-order logic or type theory (Carpenter, 1997), the domi- nant view in computational linguistics is that infer- ences based on higher-order logic are hopelessly inefficient for practical applications (Bos, 2009a). Accordingly, it is claimed that some approxima- tion of higher-order representations in terms of first-order logic (Hobbs, 1985), or a more efficient “natural logic” system based on surface structures is needed. However, it is often not a trivial task to give an approximation of rich higher-order in- formation within a first-order language (Pulman, 2007). Moreover, the coverage of existing natu- ral logic systems is limited to single-premise in- ferences (MacCartney and Manning, 2008). In this paper, we first present an improved com- positional semantics that fills the gap between the parser syntax and a composition derivation. We then develop an inference system that is capable of higher-order inferences in natural languages. We combine a state-of-the-art higher-order proof sys- tem (Coq) with a wide-coverage parser based on a modern syntactic theory (Combinatory Catego- rial Grammar, CCG). The system is designed to handle multi-premise inferences as …

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