Constituency and Dependency Relationship from a Tree Adjoining Grammar and Abstract Categorial Grammars Perspective

International Joint Conference on Natural Language Processing, pages 1257–1263, Nagoya, Japan, 14-18 October 2013. Constituency and Dependency Relationship from a Tree Adjoining Grammar and Abstract Categorial Grammar Perspective Aleksandre Maskharashvili and Sylvain Pogodalla INRIA, 54600 Villers-l`es-Nancy, France LORIA, UMR 7503, 54506 Vandœuvre-l`es-Nancy, France Sylvain.Pogodalla@inria.fr Aleksandre.Mashkharashvili@inria.fr Abstract This paper gives an Abstract Categorial Grammar (ACG) account of (Kallmeyer and Kuhlmann, 2012)’s process of trans- formation of the derivation trees of Tree Adjoining Grammar (TAG) into depen- dency trees. We make explicit how the requirement of keeping a direct interpre- tation of dependency trees into strings re- sults into lexical ambiguity. Since the ACG framework has already been used to provide a logical semantics from TAG derivation trees, we have a unified pic- ture where derivation trees and depen- dency trees are related but independent equivalent ways to account for the same surface–meaning relation. 1 Introduction Tree Adjoining Grammars (TAG) (Joshi et al., 1975; Joshi and Schabes, 1997) is a tree gram- mar formalism relying on two operations between trees: substitution and adjunction. In addition to the tree generated by a sequence of such op- erations, there is a derivation tree which records this sequence. Derivation trees soon appeared as good candidates to encode semantic-like relations between the elementary trees they glue together. However, some mismatch between these trees and the relative scoping of logical connectives and re- lational symbols, or between these trees and the dependency relations, have been observed. Solv- ing these problems often leads to modifications of derivation tree structures (Schabes and Shieber, 1994; Kallmeyer, 2002; Joshi et al., 2003; Ram- bow et al., 2001; Chen-Main and Joshi, To ap- pear). While alternative proposals have succeeded in linking derivation trees to semantic representa- tions using unification (Kallmeyer and Romero, 2004; Kallmeyer and Romero, 2007) or using an encoding (Pogodalla, 2004; Pogodalla, 2009) of TAG into the ACG framework (de Groote, 2001), only recently (Kallmeyer and Kuhlmann, 2012) has proposed a transformation from stan- dard derivation trees to dependency trees. This paper provides an ACG perspective on this transformation. The goal is twofold. First, it exhibits the underlying lexical blow up of the yield functions associated with the elementary trees in (Kallmeyer and Kuhlmann, 2012). Sec- ond, using the same framework as (Pogodalla, 2004; Pogodalla, 2009) allows us to have a shared perspective on a phrase-structure architecture and a dependency one and an equivalence on the surface-meaning relation they define. 2 Abstract Categorial Grammars ACGs provide a framework in which several grammatical formalisms may be encoded (de Groote and Pogodalla, 2004). They generate lan- guages of linear λ-terms, which generalize both string and tree languages. A key feature is to provide the user direct control over the parse structures of the grammar, the abstract language, which allows several grammatical formalisms to be defined in terms of ACG, in particular TAG (de Groote, 2002). We refer the reader to (de Groote, 2001; Pogodalla, 2009) for the details and intro- duce here only few relevant definitions and nota- tions. Definition. A higher-order …

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