Total and partial well-founded Datalog coincide

  • Jörg Flum
  • Max Kubierschky
  • Bertram Ludäscher
Contributed Papers Session 2: Logic and Databases I
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1186)


We show that the expressive power of well-founded Datalog does not decrease when restricted to total programs (it is known to decrease from Π 1 1 to Δ 1 1 on infinite Herbrand structures) thereby affirmatively answering an open question posed by Abiteboul, Hull, and Vianu [AHV95]. In particular, we show that for every well-founded Datalog program there exists an equivalent total program whose only recursive rule is of the form win(¯X) ← move(¯X,¯Y), ¬ win(¯Y) where move is definable by a quantifier-free first-order formula. This yields a nice new normal form for well-founded Datalog and implies that it is sufficient to consider draw-free games in order to evaluate arbitrary Datalog programs under the well-founded semantics.


Normal Form Logic Program Logic Programming Expressive Power Relation Symbol 
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  1. [AB94]
    K. R. Apt and R. N. Bol. Logic Programming and Negation: A Survey. Journal of Logic Programming, 19/20:9–71, 1994.Google Scholar
  2. [ABW88]
    K. R. Apt, H. Blair, and A. Walker. Towards a Theory of Declarative Knowledge. In J. Minker, editor, Foundations of Deductive Databases and Logic Programming, pages 89–148. Morgan Kaufmann, 1988.Google Scholar
  3. [AHV95]
    S. Abiteboul, R. Hull, and V. Vianu. Foundations of Databases. Addison Wesley, 1995.Google Scholar
  4. [Che95]
    W. Chen. Query Evaluation in Deductive Databases with Alternating Fixpoint Semantics. ACM Transactions on Database Systems, 20(3):239–287, 1995.Google Scholar
  5. [Dix95]
    J. Dix. Semantics of Logic Programs: Their Intuitions and Formal Properties. In A. Fuhrmann and H. Rott, editors, Logic, Action and Information. de Gruyter, 1995.Google Scholar
  6. [EF95]
    H.-D. Ebbinghaus and J. Flum. Finite Model Theory. Perspectives in Mathematical Logic. Springer, 1995.Google Scholar
  7. [Gro94]
    M. Grohe. The Structure of Fixed-Point Logics. PhD thesis, Universität Freiburg, 1994.{1,2,3}.ps.Google Scholar
  8. [Imm86]
    N. Immerman. Relational Queries Computable in Polynomial Time. Information and Control, 68:86–104, 1986.CrossRefGoogle Scholar
  9. [Kub95]
    M. Kubierschky. Remisfreie Spiele, Fixpunktlogiken und Normalformen. Master's thesis, Universität Freiburg, 1995. Scholar
  10. [Sch95]
    J. S. Schlipf. Complexity and Undecidability Results in Logic Programming. Annals of Mathematics and Artificial Intelligence, 15(III–IV), 1995.Google Scholar
  11. [VG89]
    A. Van Gelder. The Alternating Fixpoint of Logic Programs with Negation. In Proc. ACM Symposium on Principles of Database Systems, pages 1–10, 1989.Google Scholar
  12. [VG93]
    A. Van Gelder. The Alternating Fixpoint of Logic Programs with Negation. Journal of Computer and System Sciences, 47(1):185–221, 1993.Google Scholar
  13. [VGRS88]
    A. Van Gelder, K. Ross, and J. Schlipf. Unfounded Sets and Well-Founded Sematics for General Logic Programs. In Proc. ACM Symposium on Principles of Database Systems, pages 221–230, 1988.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Jörg Flum
    • 1
  • Max Kubierschky
    • 1
  • Bertram Ludäscher
    • 2
  1. 1.Mathematische FakultätUniversität FreiburgFreiburgGermany
  2. 2.Institut für InformatikUniversität FreiburgFreiburgGermany

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