Logic programming with strong negation

  • David Pearce
  • Gerd Wagner
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 475)


We show how a negation operation which allows for the possibility to represent explicit negative information can be added to Prolog without essentially altering its computational structure.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [Almukdad & Nelson 1984]
    A. Almukdad and D. Nelson: Constructible falsity and inexact predicates, JSL 49/1 (1984), 231–233Google Scholar
  2. [Belnap 1977]
    N.D. Belnap: A Useful Four-valued Logic, in G. Epstein and J.M. Dunn (eds.), Modern Uses of Many-valued Logic, Reidel, 1977, 8–37Google Scholar
  3. [Blair & Subrahmanian 1989]
    H. Blair and V.S. Subrahmanian: Paraconsistent Logic Programming, Theoretical Computer Science 68 (1989), 135–154Google Scholar
  4. [Cleave 1974]
    J.P. Cleave: The notion of logical consequence in the logic of inexact predicates, Zeitschrift für mathematische Logik und Grundlagen der Mathematik 20 (1974), 307–324Google Scholar
  5. [van Dalen 1986]
    D. van Dalen: Intuitionistic Logic, in D. Gabbay & F. Guenthner (eds.), Handbook of Philosophical Logic, Vol. III, Kluwer, Dordrecht, 1986.Google Scholar
  6. [Fitting 1986]
    M. Fitting: A Kripke-Kleene Semantics for Logic Programs, J. Logic Programming 3 (1986), 75–88.Google Scholar
  7. [Fitting 1988]
    M. Fitting: Logic Programming on a Topological Bilattice, Fund. Inf. 11 (1988), 209–218.Google Scholar
  8. [Gabbay 1988]
    D. Gabbay: What is Negation in a System?, in F.R. Drake & J.K. Truss (eds.), Logic Colloquium '86, Elsevier, Amsterdam, 1988.Google Scholar
  9. [Gabbay & Sergot 1986]
    D. Gabbay and M.J. Sergot: Negation as Inconsistency, I, J. Logic Programming 3 (1986), 1–35.Google Scholar
  10. [Hallnäs & Schroeder-Heister 1987]
    L. Hallnäs and P. Schroeder-Heister: A Proof-Theoretic Approach to Logic Programming I: Generalized Horn Clauses, SICS Research Report, 1987; forthcoming in J. Logic and Computation.Google Scholar
  11. [Kleene 1952]
    S. Kleene: Introduction to Metamathematics, Van Nostrand, 1952Google Scholar
  12. [Körner 1966]
    S. Körner: Experience and theory, Kegan Paul, London 1966Google Scholar
  13. [Lloyd & Topor 1984]
    J.W. Lloyd and R.W. Topor: Making Prolog More Expressive, JLP 1984:3, 225–240Google Scholar
  14. [Lukasiewicz 1920]
    J. Łukasiewicz: On 3-valued logic, in S. McCall (ed.): Polish Logic, Oxford University Press, 1967Google Scholar
  15. [Miller 1989]
    D. Miller: A Logical Analysis of Modules in Logic Programming, J. Logic Programming 6 (1989), 79–108.Google Scholar
  16. [Nelson 1949]
    D. Nelson: Constructible falsity, JSL 14 (1949), 16–26Google Scholar
  17. [Pearce & Wagner 1989]
    D. Pearce and G. Wagner: Reasoning with Negative Information I — Strong Negation in Logic Programs, Technical Report, Gruppe für Logik, Wissenstheorie und Information, Freie Universität Berlin, 1989Google Scholar
  18. [Przymusinksi 1989]
    T.C. Przymusinski: Non-Monotonic Formalisms and Logic Programming, in Proc. Conf. on Logic Programming 1989, MIT 1989Google Scholar
  19. [Rasiowa 1974]
    H. Rasiowa, An Algebraic Approach to Non-classical Logics, North-Holland, 1974Google Scholar
  20. [Reiter 1978]
    R. Reiter: On Closed-World Databases, in J. Minker and H. Gallaire (eds.): Logic and Databases, Plenum Press, 1978Google Scholar
  21. [Sergot, Sadri, Kowalski et al.]
    M.J. Sergot, F. Sadri, R.A. Kowalski, F. Kriwaczek, P. Hammond and H.T. Cory: The British Nationality Act as a Logic Program, Communications of the ACM 29/5 (1986), 370–386Google Scholar
  22. [Wagner 1989]
    G. Wagner: Algebraic Semantics of Propositional Logic Programs, Technical Report, Gruppe für Logik, Wissenstheorie und Information, Freie Universität Berlin, 1989Google Scholar
  23. [Wagner 1990]
    G. Wagner: The Two Sources of Nonmonotonicity in Vivid Logic — Inconsistency Handling and Weak Falsity, in G. Brewka and H. Freitag (eds.), Proceedings of the GMD Workshop on Nonmonotonic Reasoning 1989, Gesellschaft für Mathematik und Datenverarbeitung, Bonn — St. Augustin, 1990Google Scholar
  24. [Wagner 1990a]
    G. Wagner: Logic Programming with Strong Negation and Inexact Predicates, Technical Report, Gruppe für Logik, Wissenstheorie und Information, Freie Universität Berlin, 1990.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • David Pearce
    • 1
  • Gerd Wagner
    • 1
  1. 1.Gruppe für Logik, Wissenstheorie und InformationFreie Universität BerlinGermany

Personalised recommendations