Abstract
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. The main result of this paper is that the satisfiability problem of dominance constraints is NP-complete. We present two NP algorithms for solving dominance constraints, which have been implemented in the concurrent constraint programming language Oz. Despite the intractability result, the more sophisticated of our algorithms performs well in an application to scope underspecification. We also show that the positive 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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References
Backofen, R., J. Rogers, and K. Vijay-Shanker. A first-order axiomatization of the theory of finite trees. Journal of Logic, Language, and Information, 4:5–39, 1995.
Bos, J. Predicate logic unplugged. In Proceedings of the 10th Amsterdam Colloquium, pages 133–143, 1996.
Duchier, D., and C. Gardent. A constraint-based treatment of descriptions. In Proceedings of IWCS-3, Tilburg, 1999.
Duchier, D., and J. Niehren. Solving dominance constraints with finite set constraint programming. Technical report, Universität des Saarlandes, Programming Systems Lab, 1999. http://www.ps.uni-sb.de/Papers/abstracts/DomCP99.html.
Egg, M., J. Niehren, P. Ruhrberg, and F. Xu. Constraints over Lambda-Structures in Semantic Underspecification. In Proceedings COLING/ACL’98, Montreal, 1998.
Gardent, C., and B. Webber. Describing discourse semantics. In Proceedings of the 4th TAG+ Workshop, Philadelphia, 1998. University of Pennsylvania.
Johnson, D. S. A catalog of complexity classes. In Leeuwen, J. van, editor, Handbook of Theoretical Computer Science, vol A: Algorithms and Complexity, chapter 2, pages 67–161. Elsevier, 1990.
Koller, A. Constraint languages for semantic underspecification. Diplom thesis, Universität des Saarlandes, Saarbrücken, Germany, 1999. http://www.coli.uni-sb.de/~koller/papers/da.html.
Koller, A., and J. Niehren. Constraint programming in computational linguistics. Submitted. http://www.coli.uni-sb.de/~koller/cpcl.html, 1999.
Koller, A., and J. Niehren. Scope underspecification and processing. Lecture Notes, ESSLLI’ 99, Utrecht, 1999. http://www.coli.uni-sb.de/~koller/papers/esslli99.html
Marcus, M. P., D. Hindle, and M. M. Fleck. D-theory: Talking about talking about trees. In Proceedings of the 21st ACL, pages 129–136, 1983.
Meyer-Viol, W., and R. Kempson. Sequential construction of logical forms. In Proceedings of the Third Conference on Logical Aspects of Computational Linguistics, Grenoble, France, 1998.
Muskens, R. Underspecified semantics. Technical Report 95, Universität des Saarlandes, Saarbrücken, 1998. To appear.
Rabin, M. Decidability of second-order theories and automata on infinite trees. Transactions of the American Mathematical Society, 141:1–35, 1969.
Reyle, U. Dealing with ambiguities by underspecification: construction, representation, and deduction. Journal of Semantics, 10:123–179, 1993.
Rogers, J. Studies in the Logic of Trees with Applications to Grammar Formalisms. PhD thesis, University of Delaware, 1994.
Rogers, J., and K. Vijay-Shanker. Reasoning with descriptions of trees. In Proceedings of the 30th ACL, pages 72–80, University of Delaware, 1992.
Stockmeyer, L. J., and A. R. Meyer. Word problems requiring exponential time. In 5th Annual ACM Symposium on the Theory of Computing, pages 1–9, 1973.
Thatcher, J. W., and J. B. Wright. Generalized finite automata with an application to a decision problem of second-order logic. Mathematical Systems Theory, 2:57–68, 1968.
Vijay-Shanker, K. Using descriptions of trees in a tree adjoining grammar. Computational Linguistics, 18:481–518, 1992.
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Koller, A., Niehren, J., Treinen, R. (2001). Dominance Constraints: Algorithms and Complexity. In: Moortgat, M. (eds) Logical Aspects of Computational Linguistics. LACL 1998. Lecture Notes in Computer Science(), vol 2014. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45738-0_7
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DOI: https://doi.org/10.1007/3-540-45738-0_7
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