Aggregation and well-founded semantics+

  • Mauricio Osorio
  • Bharat Jayaraman
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1216)


Set-grouping and aggregation are powerful non-monotonic operations of practical interest in database query languages. We consider the problem of expressing aggregation via negation as failure (NF). We study this problem in the framework of partial-order clauses introduced in [JOM95]. We show a translation of partial-order programs to normal programs that is very natural: Any costmonotonic partial-order program P becomes a stratified normal program transl(P) such that the declarative semantics of P is equivalent to the stratified semantics of transl(P). The ability to effect such a translation is significant because the resulting normal programs do not make any explicit use of the aggregation capability, yet they are concise and intuitive. The success of this translation is due to the fact that the translated program is a stratified normal program. That would not be the case for other more general classes of programs than cost-monotonic partial-order programs. We therefore investigate a second (and more natural) translation that does not require the translated programs to be stratified, but requires the use of a suitable NF strategy. The class of normal programs originating from this translation is itself interesting. Every program in this class has a clear intended total model, although these programs are in general not stratified and not even call-consistent and do not have a stable model. The partial model given by the well-founded semantics is consistent with the intended total model and the extended well founded semantics WFS+ indeed defines the intended model. Since there is a well-defined and efficient operational semantics for partial-order programs [JOM95, JM95] we conclude that the gap between expression of a problem and computing its solution can be reduced with the right level of notation.


Partial Order Clauses Aggregation Negation as Failure Well-Founded Semantics Database Query Languages Declarative Programming Deductive Databases 


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  1. [AG91]
    S. Abiteboul and S. Grumbach, “A Rule-Based Language with Functions and Sets,” ACM Trans. on Database Systems, 16(1):1–30, 1991.CrossRefGoogle Scholar
  2. [AD94]
    C. Aranvindam and P.M. Dung, “Partial deduction of Logic Programs wrt Well-Founded Semantics,” New Generation Computing, 13 pp. 45–74, 1994Google Scholar
  3. [BN87]
    C. Beeri, S. Naqvi, et al, “Sets and Negation in a Logic Database Language (LDL1),” Proc. 6th ACM Symp. on Principles of Database Systems, pp. 21–37, 1987.Google Scholar
  4. [Dix92]
    J.Dix, “A framework for representing and characterizing semantics of Logic Programs,” Proc. 3rd Intl. Conf. on Principles of Knowledge Representation and Reasoning pp. 591–602, 1992.Google Scholar
  5. [Dix95a]
    J. Dix, “A Classification-Theory of Semantics of Normal Logic Programs: I. Strong Properties,” Fundamenta Informaticae XXII(3) pp. 227–255, 1995.Google Scholar
  6. [Dix95b]
    J. Dix, “A Classification-Theory of Semantics of Normal Logic Programs: II. Weak Properties,” Fundamenta Informaticae XXII(3) pp. 257–288, 1995.Google Scholar
  7. [GGZ91]
    G. Ganguly, S. Greco, and C. Zaniolo, “Minimum and maximum predicates in logic programs”, Proc. 10th ACM Symp. on Principles of Database Systems, pp 154–163, 1991.Google Scholar
  8. [GL88]
    Gelfond and V. Lifschitz, “The Stable Model Semantics for Logic Programming,” Proc. 5th Intl. Conf. of Logic Programming, pp. 1070–1080, Seattle, August 1988.Google Scholar
  9. [JM95]
    B. Jayaraman, and K. Moon, “Implementation of Subset-Logic Programs,” Submitted for publication.Google Scholar
  10. [JOM95]
    B. Jayaraman, M. Osorio and K. Moon, “Partial Order Programming (revisited)”, Proc. Algebraic Methodology and Software Technology, Springer-Verlag, July 1995.Google Scholar
  11. [Liu95]
    M. Liu, “Relationlog: A typed Extension to Datalog with Sets and Tuples,” Proc. Intl. Symp. of Logic Programming, pp 83–97, 1995.Google Scholar
  12. [Llo87]
    J. Lloyd, “Foundations of Logic Programming,” (2 ed.) Springer-Verlag, 1987.Google Scholar
  13. [Moo97]
    K. Moon, “Implementation of Subset Logic Languages,” Ph.D. dissertation, Department of Computer Science, SUNY-Buffalo, 1997.Google Scholar
  14. [Prz88]
    T.C. Przymusinski, “On the Declarative Semantics of Stratified Deductive Databases” in J. Minker (ed.), Foundations of Deducive Databases and Logic Programming, 1988, pp. 193–216.Google Scholar
  15. [PP90]
    T.C. Przymusinski and H. Przymusinska, “Semantic Issues in Deductive Databases and Logic Programs” in R.B. Banerji (ed.), Formal Techniques in Artificial Intelligence, 1990, pp. 321–367.Google Scholar
  16. [RS92]
    K.A. Ross and Y. Sagiv, “Monotonic Aggregation in Deductive Databases,” Proc. 11th ACM Symp. on Principles of Database Systems, pp. 114–126, San Diego, 1992.Google Scholar
  17. [Sch92b]
    J. Schlipf, “Formalizing a Logic for Logic Programming”, Annals of Mathematics and Artificial Intelligence, 5:279–302, 1992.Google Scholar
  18. [SZ90]
    D. Sacca and C. Zaniolo, “Stable models and non-determinism in logic programs with negation”, Proc. 9th ACM Symp. on Principles of Database Systems, 1990, pp. 205–217.Google Scholar
  19. [Van92]
    A. Van Gelder, “The Well-Founded Semantics of Aggregation,” Proc. ACM 11th Principles of Database Systems, pp. 127–138, San Diego, 1992.Google Scholar
  20. [VRS91]
    A. Van Gelder, K.A. Ross, and J.S. Schlipf, “The Well-Founded Semantics for General Logic Programs,” JACM, 38(3):620–650.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Mauricio Osorio
    • 1
  • Bharat Jayaraman
    • 2
  1. 1.Departamento de Ingenieria en Sistemas ComputacionalesUniversidad de las AmericasCholulaMexico
  2. 2.Department of Computer ScienceState University of New York at BuffaloBuffaloUSA

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