Dominance constraints for finite tree structures are widely used in several areas of computational linguistics including syntax, semantics, and discourse. In this paper, we investigate algorithmic and complexity questions for dominance constraints and their first-order theory. We present two NP algorithms for solving dominance constraints, which have been implemented in the concurrent constraint programming language Oz. The main result of this paper is that the satisfiability problem of dominance constraints is NP-complete. Despite this intractability result, the more sophisticated of our algorithms performs well in an application to scope underspecification. We also show that the existential fragment of the first-order theory of dominance constraints is NP-complete and that the full first-order theory has non-elementary complexity.

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Dominance constraints are logical descriptions of trees that are widely used in computational linguistics. Their general satisfiability problem is known to be NP-complete. Here we identify normal dominance constraints and present an efficient graph algorithm for testing their satisfiablity in deterministic polynomial time. Previously, no polynomial time algorithm was known.

this paper I shall give a set of simple LFG-like annotated phrase structure rules which connect underspecified representations with other components of the grammar. The rules may be traversed in any order. The underspecified representations will be much like the UDRSs of Reyle [1992], but will formally consist of two parts: (a) a set of equations in ordinary classical type logic with abbreviations that emulate the language of Discourse Representation Theory, and (b) a set of descriptions in the first-order language of trees. Both parts will be generated by the grammar in a relatively independent way. The first part will give us building blocks of `open' Discourse Representation Structures. The second part will summarise all possible ways in which these building blocks may be combined into an ordinary DRS

Both in computational linguistics and in formal semantics, descriptions have been used which are stated in terms of dominance. Yet the issue of how such descriptions are processed has been little explored. In this paper, we present a constraint-based treatment of descriptions and apply it to the description-based treatment of discourse advocated in [GW98a].

Recent developments in connectionist architectures for symbolic computation have made it possible to investigate parsing in a connectionist network while still taking advantage of the large body of work on parsing in symbolic frameworks. The work discussed here investigates syntactic parsing in the temporal synchrony variable binding model of symbolic computation in a connectionist network. This computational architecture solves the basic problem with previous connectionist architectures, while keeping their advantages. However, the architecture does have some limitations, which impose constraints on parsing in this architecture. Despite these constraints, the architecture is computationally adequate for syntactic parsing. In addition, the constraints make some significant linguistic predictions. These arguments are made using a specific parsing model. The extensive use of partial descriptions of phrase structure trees is crucial to the ability of this model to recover the syntactic st...

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.

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Dominance constraints are widely used in computational linguistics as a language for talking and reasoning about trees. In this paper, we extend dominance constraints by admitting set operators. We present a solver for dominance constraints with set operators, which is based on propagation and distribution rules, and prove its soundness and completeness.

Dominance constraints are logical descriptions of trees that are widely used in computational linguistics. Their general