Hypothetical datalog: Complexity and expressibility

  • Anthony J. Bonner
Complexity And Optimization
Part of the Lecture Notes in Computer Science book series (LNCS, volume 326)

Abstract

We present an extension of Horn-clause logic which can hypothetically add and delete tuples from a database. Such logics have been discussed in the literature, but their complexities and expressibilities have remained an open question. This paper examines two such logics in the function-free, predicate case. It is shown, in particular, that augmenting Horn-clause logic with hypothetical addition increases its data-complexity from PTIME to PSPACE. When deletions are added as well, complexity increases again, to EXPTIME. To establish expressibility, we augment the logic with negation-by-failure and view it as a query language for relational databases. The logic of hypothetical additions then expresses all database queries which are computable in PSPACE. When deletions are included, the logic expresses all database queries computable in EXPTIME.

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References

  1. [1]
    S. Abiteboul and V. Vianu. A Transaction Language Complete for Database Update Specification. In Proceedings of the ACM Symposium on the Principles of Database Systems, pages 260–268, 1987.Google Scholar
  2. [2]
    K.R. Apt, H.A. Blair, and A. Walker. Towards a Theory of Declarative Knowledge. In Jack Minker, editor, Foundations of Deductive Databases and Logic Programming, chapter 2, pages 89–148, Morgan Kaufmann, 1988.Google Scholar
  3. [3]
    K.R. Apt and M.H. Van Emden. Contributions to the Theory of Logic Programming. Journal of the ACM, 29(3):841–862, 1982.CrossRefGoogle Scholar
  4. [4]
    A.J. Bonner. A Logic for Hypothetical Reasoning. In Proceedings of the Seventh National Conference on Artificial Intelligence, American Association for Artificial Intelligence, August 1988.Google Scholar
  5. [5]
    A.J. Bonner. Hypothetical Datalog: Complexity and Expressibility. Technical Report DCS-TR-231, Department of Computer Science, Rutgers university, New Brunswick, NJ 08903, 1988.Google Scholar
  6. [6]
    A.J. Bonner. Hypothetical Datalog: Complexity and Expressibility. In Proceedings of the Second International Conference on Database Theory, Bruges, Belgium, August 31-September 2 1988.Google Scholar
  7. [7]
    A.J. Bonner. A Logic for Hypothetical Reasoning. Technical Report DCS-TR-230, Department of Computer Science, Rutgers University, New Brunswick, NJ 08903, 1988.Google Scholar
  8. [8]
    A.K. Chandra and D. Harel. “Computable Queries for Relational Databases”. Journal of Computer and Systems Science, 21(2):156–178, 1980.Google Scholar
  9. [9]
    A.K. Chandra and D. Harel. “Horn Clauses and the Fixpoint Hierarchy”. In Proceedings of the ACM Symposium on the Principles of Database Systems, pages 158–163, 1982.Google Scholar
  10. [10]
    A.K. Chandra and D. Harel. “Structure and Complexity of Relational Queries”. In Proceedings of the Symposium on the Foundations of Computer Science, pages 333–347, 1980.Google Scholar
  11. [11]
    A.K. Chandra, D. Kozen, and L.J. Stockmeyer. “Alternation”. Journal of the ACM, 114–133, 1981.Google Scholar
  12. [12]
    A.K. Chandra and L.J. Stockmeyer. “Alternation”. In Proceedings of the Symposium on the Foundations of Computer Science, pages 98–108, 1976.Google Scholar
  13. [13]
    M.C. Fitting. Intuitionistic Logic, Model Theory and Forcing. North-Holland, 1969.Google Scholar
  14. [14]
    D.M. Gabbay. “N-Prolog: an Extension of Prolog with Hypothetical Implications. II. Logical Foundations and Negation as Failure”. Journal of Logic Programming, 2(4):251–283, 1985.Google Scholar
  15. [15]
    D.M. Gabbay and U. Reyle. “N-Prolog: an Extension of Prolog with Hypothetical Implications. I”. Journal of Logic Programming, 1(4):319–355, 1984.CrossRefGoogle Scholar
  16. [16]
    D. Harel. First-Order Dynamic Logic. Volume 68 of Lecture Notes in Computer Science, Springer Verlag, 1979.Google Scholar
  17. [17]
    J.E. Hopcroft and J.D. Ullman. Introduction to Automata Theory, Languages and Computation. Addison-Wesley, 1979.Google Scholar
  18. [18]
    N. Immerman. Relational Queries Computable in Polynomial Time. In Proceedings of the Symposium on the Foundations of Computer Science, pages 147–152, 1982.Google Scholar
  19. [19]
    R. Kowalski. Logic for Problem Solving. North-Holland, 1979.Google Scholar
  20. [20]
    R.E. Ladner. The Computational Complexity of Provability in Systems of Propositional Modal Logic. SIAM Journal of Computing, 6(3):467–480, 1977.Google Scholar
  21. [21]
    S. Manchanda and D.S. Warren. A Logic-based Language for Database Updates. In Jack Minker, editor, Foundations of Deductive Databases and Logic Programming, chapter 10, pages 363–394, Morgan Kaufmann, 1988.Google Scholar
  22. [22]
    L.T. McCarty. “Clausal Intuitionistic Logic. I. Fixed-Point Semantics”. Journal of Logic Programming, 5(1):1–31, 1988.Google Scholar
  23. [23]
    L.T. McCarty. Clausal Intuitionistic Logic. II. Tableau Proof Procedures. Journal of Logic Programming, 1988. To appear.Google Scholar
  24. [24]
    D. Miller. A Logical Analysis of Modules in Logic Programming. In Proceedings of the IEEE Symposium on Logic Programming, 1986.Google Scholar
  25. [25]
    R. Statman. Intuitionistic Propositional Logic is Polynomial-Space complete. Theoretical Computer Science, 9(1):67–72, 1979.Google Scholar
  26. [26]
    M.H. Van Emden and R.A. Kowalski. The Semantics of Predicate Logic as a Programming Language. Journal of the ACM, 23(4):733–742, 1976.CrossRefGoogle Scholar
  27. [27]
    M. Vardi. Relational Queries Computable in Polynomial Time. In Proceedings of the Symposium on the Foundations of Computer Science, pages 137–145, 1982.Google Scholar
  28. [28]
    M. Vardi. The Complexity of Relational Query Languages. In Proceedings of the ACM Symposium on the Principles of Database Systems, pages 137–146, 1982.Google Scholar
  29. [29]
    D.S. Warren. Database Updates in Pure Prolog. In Proceedings of the International Conference on Fifth Generation Computer Systems, pages 244–253, 1984.Google Scholar

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Anthony J. Bonner
    • 1
  1. 1.Department of Computer ScienceRutgers UniversityNew Brunswick

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