Optimality parsing and local cost functions in Discontinuous Grammar

After a brief survey of Discontinuous Grammar (DG), we propose local cost functions as a generalization of violable constraints in OT, probabilities in PCFG, and processing times in distributed competition models. We demonstrate how local cost functions can be used in DG to encode violable constraints on word order, landing sites, islands, agreement, and selectional restrictions, as well as lexical frequencies and pragmatic preferences. Rephrasing parsing as an optimization problem in which a large space of partial parses is searched for a minimum-cost solution, we propose a heuristic parsing algorithm for DG based on local search, with worst-case complexity O(n log4 n) given linguistically reasonable assumptions on tree depth and island constraints, and O(n5) without any assumptions. The proposed algorithm works in the presence of local ambiguity, produces the right analysis for a wide range of discontinuous word-order phenomena such as topicalizations, relativizations, extractions, scramblings, and discontinuous APs, and fails on garden-path sentences, just like humans. 1 Discontinuous Grammar Discontinuous Grammar [10] (or DG) is a syntax formalism that was originally conceived as a synthesis between Head-Driven Phrase Structure Grammar [15], Government & Binding [5], and German dependency grammar [6]. Subsequently, it has borrowed ideas from Optimality Theory [8], Tree-Adjoining Grammar [1], 1 Email: [email protected]. Web: www.id.cbs.dk/∼mtk/dg 2 I wish to thank my thesis advisor, Professor Carl Vikner, to whom this paper is dedicated. Thanks also to Richard Hudson, Don C. Mitchell, Owen Rambow, Lars Konieczny, Line Mikkelsen, Sten Vikner, Sabine Kirchmeyer-Andersen, and Alex Klinge for fruitful discussions, and to two anonymous reviewers for highly valuable comments. This work was made possible by a grant from the Danish Research Council for the Humanities. c ©2001 Published by Elsevier Science B. V.