Highly Constrained Unification Grammars

Unification grammars are widely accepted as an expressive means for describing the structure of natural languages. In general, the recognition problem is undecidable for unification grammars. Even with restricted variants of the formalism, off-line parsable grammars, the problem is computationally hard. We present two natural constraints on unification grammars which limit their expressivity and allow for efficient processing. We first show that non-reentrant unification grammars generate exactly the class of context-free languages. We then relax the constraint and show that one-reentrant unification grammars generate exactly the class of mildly context-sensitive languages. We thus relate the commonly used and linguistically motivated formalism of unification grammars to more restricted, computationally tractable classes of languages.

[1]  Mark Johnson,et al.  Finite-state Approximation of Constraint-based Grammars using Left-corner Grammar Transforms , 1998, ACL.

[2]  David J. Weir,et al.  The equivalence of four extensions of context-free grammars , 1994, Mathematical systems theory.

[3]  Martin Kay,et al.  Syntactic Process , 1979, ACL.

[4]  Hans-Ulrich Krieger,et al.  A context-free superset approximation of unification-based grammars , 2004 .

[5]  Nissim Francez,et al.  Unification Grammars and Off-Line Parsability , 2005, J. Log. Lang. Inf..

[6]  Bill Keller,et al.  A Tractable Extension of Linear Indexed Grammars , 1995, EACL.

[7]  Mark Johnson,et al.  Attribute-value logic and the theory of grammar , 1988 .

[8]  Ruslan Mitkov,et al.  The Oxford handbook of computational linguistics , 2003 .

[9]  S. Wintner.  Unification: Computational Issues , 2006 .

[10]  Aravind K. Joshi,et al.  Tree-Adjoining Grammars , 1997, Handbook of Formal Languages.

[11]  Shuly Wintner,et al.  Highly Constrained Unification Grammars , 2006, ACL.

[12]  Beth Ann Hockey,et al.  A baseline method for compiling typed unification grammars into context free language models , 2001, INTERSPEECH.

[13]  Stuart M. Shieber,et al.  Constraint-based grammar formalisms , 1992 .

[14]  David J. Weir,et al.  Parsing Some Constrained Grammar Formalisms , 1993, Comput. Linguistics.

[15]  Giorgio Satta,et al.  Tree-Adjoining Grammar Parsing and Boolean Matrix Multiplication , 1994, Comput. Linguistics.

[16]  Bob Carpenter.  Logic of Typed Feature Structures, The (Cambridge Tracts in Theoretical Computer Science) , 2005 .

[17]  Bob Carpenter,et al.  The logic of typed feature structures , 1992 .

[18]  Rebecca N. Wright,et al.  Finite-State Approximation of Phrase Structure Grammars , 1991, ACL.

[19]  Aravind K. Joshi,et al.  Tree Adjunct Grammars , 1975, J. Comput. Syst. Sci..

[20]  Raffaella Bernardi,et al.  The Syntactic Process: Language, Speech, and Communication, Mark Steedman , 2004, J. Log. Lang. Inf..

[21]  David J. Weir.  A Geometric Hierarchy Beyond Context-Free Languages , 1992, Theor. Comput. Sci..

[22]  Walter J. Savitch,et al.  The Formal Complexity of Natural Language , 1987 .

[23]  Gerald Gazdar,et al.  Applicability of Indexed Grammars to Natural Languages , 1988 .

[24]  N. Curteanu.  Book Reviews: Lecture on Contemporary Syntactic Theories: An Introduction to Unification-Based Approaches to Grammar , 1987, CL.

[25]  John Michael Robson,et al.  The Complexity of Go , 1983, IFIP Congress.

[26]  Carl Jesse Pollard,et al.  Generalized phrase structure grammars, head grammars, and natural language , 1984 .

[27]  Shuly Wintner,et al.  Introduction to Unification Grammars , 2006, Recent Advances in Formal Languages and Applications.