Logical Inference on Dependency-based Compositional Semantics

Proceedings of the 52nd Annual Meeting of the Association for Computational Linguistics, pages 79–89, Baltimore, Maryland, USA, June 23-25 2014. c⃝2014 Association for Computational Linguistics Logical Inference on Dependency-based Compositional Semantics Ran Tian Yusuke Miyao Takuya Matsuzaki National Institute of Informatics, Japan {tianran,yusuke,takuya-matsuzaki}@nii.ac.jp Abstract Dependency-based Compositional Se- mantics (DCS) is a framework of natural language semantics with easy-to-process structures as well as strict semantics. In this paper, we equip the DCS framework with logical inference, by defining ab- stract denotations as an abstraction of the computing process of denotations in original DCS. An inference engine is built to achieve inference on abstract denota- tions. Furthermore, we propose a way to generate on-the-fly knowledge in logical inference, by combining our framework with the idea of tree transformation. Experiments on FraCaS and PASCAL RTE datasets show promising results. 1 Introduction Dependency-based Compositional Semantics (DCS) provides an intuitive way to model seman- tics of questions, by using simple dependency-like trees (Liang et al., 2011). It is expressive enough to represent complex natural language queries on a relational database, yet simple enough to be latently learned from question-answer pairs. In this paper, we equip DCS with logical inference, which, in one point of view, is “the best way of testing an NLP system’s semantic capacity” (Cooper et al., 1996). It should be noted that, however, a framework primarily designed for question answering is not readily suited for logical inference. Because, an- swers returned by a query depend on the specific database, but implication is independent of any databases. For example, answers to the question “What books are read by students?”, should al- ways be a subset of answers to “What books are ever read by anyone?”, no matter how we store the data of students and how many records of books are there in our database. Thus, our first step is to fix a notation which ab- stracts the calculation process of DCS trees, so as to clarify its meaning without the aid of any exist- ing database. The idea is to borrow a minimal set of operators from relational algebra (Codd, 1970), which is already able to formulate the calculation in DCS and define abstract denotation, which is an abstraction of the computation of denotations guided by DCS trees. Meanings of sentences then can be represented by primary relations among abstract denotations. This formulation keeps the simpleness and computability of DCS trees mostly unaffected; for example, our semantic calculation for DCS trees is parallel to the denotation compu- tation in original DCS. An inference engine is built to handle inference on abstract denotations. Moreover, to compensate the lack of background knowledge in practical in- ference, we combine our framework with the idea of tree transformation (Bar-Haim et al., 2007), to propose a way of generating knowledge in logical representation from entailment rules (Szpektor et al., 2007), which are by now typically considered as syntactic rewriting rules. We test our system on FraCaS (Cooper et al., 1996) and PASCAL RTE datasets (Dagan et al., …

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