Learning Synchronous Grammars for Semantic Parsing with Lambda Calculus

Proceedings of the 45th Annual Meeting of the Association of Computational Linguistics, pages 960–967, Prague, Czech Republic, June 2007. c⃝2007 Association for Computational Linguistics Learning Synchronous Grammars for Semantic Parsing with Lambda Calculus Yuk Wah Wong and Raymond J. Mooney Department of Computer Sciences The University of Texas at Austin {ywwong,mooney}@cs.utexas.edu Abstract This paper presents the first empirical results to our knowledge on learning synchronous grammars that generate logical forms. Using statistical machine translation techniques, a semantic parser based on a synchronous context-free grammar augmented with λ- operators is learned given a set of training sentences and their correct logical forms. The resulting parser is shown to be the best- performing system so far in a database query domain. 1 Introduction Originally developed as a theory of compiling pro- gramming languages (Aho and Ullman, 1972), syn- chronous grammars have seen a surge of interest re- cently in the statistical machine translation (SMT) community as a way of formalizing syntax-based translation models between natural languages (NL). In generating multiple parse trees in a single deriva- tion, synchronous grammars are ideal for model- ing syntax-based translation because they describe not only the hierarchical structures of a sentence and its translation, but also the exact correspon- dence between their sub-parts. Among the gram- mar formalisms successfully put into use in syntax- based SMT are synchronous context-free gram- mars (SCFG) (Wu, 1997) and synchronous tree- substitution grammars (STSG) (Yamada and Knight, 2001). Both formalisms have led to SMT sys- tems whose performance is state-of-the-art (Chiang, 2005; Galley et al., 2006). Synchronous grammars have also been used in other NLP tasks, most notably semantic parsing, which is the construction of a complete, formal meaning representation (MR) of an NL sentence. In our previous work (Wong and Mooney, 2006), se- mantic parsing is cast as a machine translation task, where an SCFG is used to model the translation of an NL into a formal meaning-representation lan- guage (MRL). Our algorithm, WASP, uses statistical models developed for syntax-based SMT for lexical learning and parse disambiguation. The result is a robust semantic parser that gives good performance in various domains. More recently, we show that our SCFG-based parser can be inverted to produce a state-of-the-art NL generator, where a formal MRL is translated into an NL (Wong and Mooney, 2007). Currently, the use of learned synchronous gram- mars in semantic parsing and NL generation is lim- ited to simple MRLs that are free of logical vari- ables. This is because grammar formalisms such as SCFG do not have a principled mechanism for han- dling logical variables. This is unfortunate because most existing work on computational semantics is based on predicate logic, where logical variables play an important role (Blackburn and Bos, 2005). For some domains, this problem can be avoided by transforming a logical language into a variable-free, functional language (e.g. the GEOQUERY functional query language in Wong and Mooney (2006)). How- ever, development of such a functional language is non-trivial, and as we will see, logical languages …

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