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Workshop on Information Systems and Artificial Intelligence

IS/KI 1994: Management and Processing of Complex Data Structures pp 83–103Cite as

Expressive power and complexity of disjunctive datalog under the stable model semantics

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 777))

Abstract

DATALOG¬ is a well-known logical query language, whose expressive power and data complexity under the stable model semantics has been recently determined. In this paper we consider the extension of DATALOG¬ to disjunctive DATALOG¬ (DDL¬), which allows disjunction in the head of program clauses, under the stable model semantics. We investigate and determine the expressiveness and the data complexity of DDL¬, as well as the expression complexity. The main findings of this paper are that disjunctive datalog captures precisely the class of all ∑ p2 -recognizable queries under the brave version of reasoning, and symmetrically the class of all Π p2 -recognizable queries under the cautious version; the data complexity is ∑ p2 -completeness in the brave version, and Π p2 -complete in the cautious version, while the expression complexity is NEXPTIMENP-complete in the brave version and co-NEXPTIMENPcomplete in the cautious version.

The main part of this work has been carried out while this author, on leave from the University of Helsinki, was spending a sabbatical at the TU Vienna in spring 1993.

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References

  1. J. Balcázar, J. Diaz, and J. Gabarró. Structural Complexity I. Springer, 1988.

    Google Scholar 

  2. J. Balcázar, A. Lozano, and J. Torán. The Complexity of Algorithmic Problems on Succinct Instances. In R. Baeta-Yates and U. Manber, editors, Computer Science, pages 351–377. Plenum Press, New York, 1992.

    Google Scholar 

  3. S. Ceri, G. Gottlob, and L. Tanca. Logical Programming and Databases. Springer, 1990.

    Google Scholar 

  4. A. Chandra and D. Harel. Computable Queries for Relational Databases. Journal of Computer and System Sciences, 21:156–178, 1980.

    Google Scholar 

  5. A. Chandra and D. Harel. Horn Clause Queries and Generalizations. Journal of Logic Programming, 2:1–15, 1985.

    Google Scholar 

  6. C. C. Chang and H. J. Keisler. Model Theory. North-Holland, 2nd edition, 1973.

    Google Scholar 

  7. T. Eiter and G. Gottlob. Complexity Aspects of Various Semantics for Disjunctive Databases. In Proceedings of the Twelth ACM SIGACT SIGMOD-SIGART Symposium on Principles of Database Systems (PODS-93), pages 158–167, 1993.

    Google Scholar 

  8. T. Eiter, G. Gottlob, and H. Mannila. Adding Disjunction to Datalog. Manuscript available from the authors, November 1993.

    Google Scholar 

  9. R. Fagin. Generalized First-Order Spectra and Polynomial-Time Recognizable Sets. In R. M. Karp, editor, Complexity of Computation, pages 43–74. AMS, 1974.

    Google Scholar 

  10. J. Fernández and J. Minker. Semantics of Disjunctive Deductive Databases. In Proceedings of the International Conference on Database Theory (ICDT-92), pages 21–50, Berlin, October 1992.

    Google Scholar 

  11. H. Galperin and A. Wigderson. Succinct Representations of Graphs. Information and Computation, 56:183–198, 1983.

    Google Scholar 

  12. M. Garey and D. S. Johnson. Computers and Intractability — A Guide to the Theory of NP-Completeness. W. H. Freeman, New York, 1979.

    Google Scholar 

  13. Y. Gurevich. Logic and the Challenge of Computer Science. In E. Börger, editor, Trends in Theoretical Computer Science, chapter 1. Computer Science Press, 1988.

    Google Scholar 

  14. D. S. Johnson. A Catalog of Complexity Classes. volume A of Handbook of Theoretical Computer Science, chapter 2. Elsevier Science Publishers B.V. (North-Holland), 1990.

    Google Scholar 

  15. P. Kolaitis and C. H. Papadimitriou. Why Not Negation By Fixpoint? Journal of Computer and System Sciences, 43:125–144, 1991.

    Google Scholar 

  16. J. Lobo, J. Minker, and A. Rajasekar. Foundations of Disjunctive Logic Programming. MIT Press, Cambridge, MA, 1992.

    Google Scholar 

  17. A. Lozano and J. Balcázar. The Complexity of Graph Problems for Succinctly Represented Graphs. In Proceedings of the 15th Intl. Workshop on Graph-Theoretic Concepts in Computer Science, number 411 in LNCS, pages 277–286, Castle Rolduc, The Netherlands 1989.

    Google Scholar 

  18. J. Lynch. Complexity Classes and Theories of Finite Models. Mathematical Systems Theory, 15:127–144, 1982.

    Google Scholar 

  19. J. Makowsky. Model Theory and Computer Science: An Appetizer. In S. Abramsky, D. Gabbay, and T. Maibaum, editors, Handbook of Logic in Computer Science, volume I, chapter 6. Oxford University Press, 1992.

    Google Scholar 

  20. W. Marek, A. Nerode, and J. Remmel. A Theory of Nonmonotonic Rule Systems II. Annals of Mathematics and Artificial Intelligence, 5:229–264, 1992.

    Google Scholar 

  21. W. Marek, A. Nerode, and J. Remmel. How Complicated is the Set of Stable Models of a Recursive Logic Program? Annals of Pure and Applied Logic, 56:119, 1992.

    Google Scholar 

  22. W. Marek and M. Truszczyński. Autoepistemic Logic. Journal of the ACM, 38(3):588–619, 1991.

    Google Scholar 

  23. W. Marek and M. Truszczyński. Computing Intersection of Autoepistemic Expansions. In Proceedings of the 1st Intl. Workshop on Logic Programming and Nonmonotonic Reasoning, pages 37–50, Washington DC, July 1991. MIT Press.

    Google Scholar 

  24. J. McCarthy. Circumscription — A Form of Non-Monotonic Reasoning. Artificial Intelligence, 13:27–39, 1980.

    Google Scholar 

  25. J. Minker. On Indefinite Data Bases and the Closed World Assumption. In Proceedings of the 6th Conference on Automated Deduction (CADE), pages 292–308, 1982.

    Google Scholar 

  26. C. Papadimitriou and M. Yannakakis. A Note on Succinct Representations of Graphs. Information and Computation, 71:181–185, 1985.

    Google Scholar 

  27. T. Przymusinski. On the Declarative and Procedural Semantics of Stratified Deductive Databases. In J. Minker, editor, Foundations of Deductive Databases and Logic Programming, pages 193–216. Morgan Kaufman, Washington DC, 1988.

    Google Scholar 

  28. T. Przymusinski. Stable Semantics for Disjunctive Programs. New Generation Computing, 9:401–424, 1991.

    Google Scholar 

  29. D. Saccà. Multiple Stable Models are Needed to Solve Unique Solution Problems. In Informal Proceedings of the Second Compulog Net Meeting on Knowledge Bases (CNKBS-93), Athens, April 1993.

    Google Scholar 

  30. J. Schlipf. The Expressive Powers of Logic Programming Semantics. Technical Report CIS-TR-90-3, Computer Science Department, University of Cincinnati, 1990. Submitted. A preliminary version of this paper appeared in: Proceedings PODS-90, pages 196–204.

    Google Scholar 

  31. J. Schlipf. A Survey of Complexity and Undecidability Results in Logic Programming. In H. Blair, W. Marek, A. Nerode, and J. Remmel, editors, Informal Proceedings of the Workshop on Structural Complexity and Recursion-Theoretic Methods in Logic Programming, pages 93–102, Washington DC, November 1992. Cornell University, Mathematical Sciences Institute.

    Google Scholar 

  32. I. Stewart. Complete Problems Involving Boolean Labelled Structures and Projection Transactions. Journal of Logic and Computation, 1(6):861–882, 1991.

    Google Scholar 

  33. L. J. Stockmeyer. The Polynomial-Time Hierarchy. Theoretical Computer Science, 3:1–22, 1977.

    Google Scholar 

  34. J. D. Ullman. Principles of Database and Knowledge Base Systems, volume 1. Computer Science Press, 1988.

    Google Scholar 

  35. M. Vardi. Complexity of relational query languages. In Proceedings of the 14th ACM SIGACT Symposium on Theory of Computing (STOC-82), pages 137–146, 1982.

    Google Scholar 

  36. A. Yahya and L. Henschen. Deduction in Non-Horn Databases. Journal of Automated Reasoning, 1(2):141–160, 1985.

    Google Scholar 

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Authors and Affiliations

  1. Christian Doppler Labor für Expertensysteme Institut für Informationssysteme, Technische Universität Wien, Paniglgasse 16, 1040, Wien, Austria

    Thomas Eiter, Georg Gottlob & Heikki Mannila

Authors
  1. Thomas Eiter
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  2. Georg Gottlob
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  3. Heikki Mannila
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Kai von Luck Heinz Marburger

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© 1994 Springer-Verlag Berlin Heidelberg

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Eiter, T., Gottlob, G., Mannila, H. (1994). Expressive power and complexity of disjunctive datalog under the stable model semantics. In: von Luck, K., Marburger, H. (eds) Management and Processing of Complex Data Structures. IS/KI 1994. Lecture Notes in Computer Science, vol 777. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57802-1_5

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  • DOI: https://doi.org/10.1007/3-540-57802-1_5

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57802-4

  • Online ISBN: 978-3-540-48335-9

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