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We examine the consistency problem for descriptions of trees based on remote dominance, and present a consistency-checking algorithm which is polynomial in the number of nodes in the description, despite disjunctions inherent in the theory of trees. The resulting algorithm allows for descriptions which go beyond sets of atomic formulas to allow certain types of disjunction and negation. collections to be combined contain contradictory information. | ON DETERMINING THE CONSISTENCY OF PARTIAL DESCRIPTIONS OF TREES Thomas L. Cornell Cognitive Science Program University of Arizona Tucson AZ 85721 cornell@ccit.arizona.edu Abstract1 We examine the consistency problem for descriptions of trees based on remote dominance and present a consistency-checking algorithm which is polynomial in the number of nodes in the description despite disjunctions inherent in the theory of trees. The resulting algorithm allows for descriptions which go beyond sets of atomic formulas to allow certain types of disjunction and negation. INTRODUCTION In Marcus Hindle Fleck 1983 the authors proposed an approach to syntactic tree structures which took the primary structural relation to be remote dominance rather than immediate dominance. Recently researchers have shown a revived interest in variants of Marcus et al. s D-Theory most likely due to the availability of approaches and techniques developed in the study of feature structures and their underlying logics. For example both Rogers Vijay-Shanker 1992 and Cornell 1992 present formal treatments of many notions which Marcus et al. 1983 treated only informally and incompletely. Furthermore work on the psycholinguistic implications of this approach has continued apace Weinberg 1988 Gorrell 1991 Marcus Hindle 1990 making all the more necessary sustained foundational work in the theory of description-based tree-building applications parsers generators etc. This paper addresses one particular problem that arises in this approach to tree building. As with feature-structures the essential operation here is the combination of two collections of partial information about the syntactic structure of an expression. It may happen that the two 1 Many thanks to Dick Oehrle Ed Stabler Drew Moshier and Mark Johnson for comments discussion and encouragement. Theirs the gratitude mine the fault. collections to be combined contain contradictory information. For example one might contain the assertion that node
