Reasoning with negative information, II: Hard negation, strong negation and logic programs

  • David Pearce
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 619)


In the framework of extended logic programming we propose a criterion by which a negation operator can be said to express explicit falsity. We show that a certain system of constructive logic with strong negation, due to López-Escobar (1972) and Almukdad & Nelson (1984), fulfils this criterion, as do several recent systems of logic programming, including that of Gelfond & Lifschitz (1990). We use these facts to infer that, from a logical point of view, the programming systems in question can be viewed as subsystems of constructive logic.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Akama, S, On the Proof Method for Constructive Falsity, Zeit. math. Logik & Grundlagen d. Math. 34 (1988), 385–392.Google Scholar
  2. Almukdad, D & Nelson, D, Constructible Falsity and Inexact Predicates, J Symbolic Logic 49 (1984), 231–233.Google Scholar
  3. Cellucci, C., Using Full First-Order Logic as a Programming Language, in Proc. Logic and Computer Sciences 1986, Rend. Sem. Mat. Univ. Pol. Torino, 1987.Google Scholar
  4. Fitting, M, A Kripke-Kleene Semantics for Logic Programs, J Logic Programming 3 (1986), 75–88.Google Scholar
  5. Gabbay, D & Sergot, M, Negation as Inconsistency, J Logic Programming 3 (1986), 1–35.Google Scholar
  6. Gelfond, M & Lifschitz, V, The Stable Model Semantics for Logic Programming, in Kowalski, R & Bowen, K, (Eds), Proc. ICLP-88, MIT Press, 1988, 1070–1080.Google Scholar
  7. Gelfond, M & Lifschitz, V, Logic Programs with Classical Negation, in Warren, D & Szeredi, P, (Eds), Proc. ICLP-90, MIT Press, 1990, 579–597.Google Scholar
  8. Gurevich, Y, Intuitionistic Logic with Strong Negation, Studia Logica 36 (1977), 49–59.Google Scholar
  9. Hallnäs, L & Schroeder-Heister, P, A Proof-Theoretic Approach to Logic Programming, J Logic and Computation 1(1990).Google Scholar
  10. Kowalski, R & Sadri, F, Logic Programs with Exceptions, in Warren, D & Szeredi, P, (Eds.), Proc. ICLP-90, MIT Press, 1990.Google Scholar
  11. Kutschera, F, Ein verallgemeinerter Widerlegungsbegriff für Gentzenkalküle, Arch. Math. Logik 12 (1969), 104–118.Google Scholar
  12. Levesque, H, Making Believers out of Computers, Artificial Intelligence 30 (1986), 81–107.Google Scholar
  13. López-Escobar, E G K, Refutability and Elementary Number Theory, Indag. Math. 34 (1972), 362–374.Google Scholar
  14. Lu, J & Subrahmanian, V, Protected Completions of First-Order General Logic Programs, J Automated Reasoning 6 (1990), 147–172.Google Scholar
  15. Miller, D, A Logical Analysis of Modules in Logic Programming, J Logic Programming 6 (1989), 79–108.Google Scholar
  16. Nelson, D, Constructible Falsity, J Symbolic Logic 14 (1949), 16–26.Google Scholar
  17. Nelson, D, Negation and Separation of Concepts in Constructive Systems, in Heyting, A (Ed), Constructivity in Mathematics, North-Holland, Amsterdam, 1959.Google Scholar
  18. Pearce, D & Wagner, G, Reasoning with Negative Information, I: Strong Negation in Logic Programs, in Haaparanta, L, Kusch, M, & Niiniluoto, I, (eds.), Language, Knowledge, and Intentionality, (Acta Philosophica Fennica 49), Helsinki, 1990, 430–453.Google Scholar
  19. Pearce, D & Wagner, G, Logic Programming with Strong Negation, in Schroeder-Heister, P, (Ed), Extensions of Logic Programming, Lecture Notes in AI, Vol. 475, Springer-Verlag, Berlin etc, 1991, 311–326.Google Scholar
  20. Poole, D & Goebel, R, Gracefully Adding Negation and Disjunction to Prolog, Proc. ICLP-86, MIT Press, 1986.Google Scholar
  21. Przymusinski, T, Perfect Model Semantics, in Kowalski, R, & Bowen, K, (Eds.), Proc. ICLP-88, MIT Press, 1988.Google Scholar
  22. Reiter, R, A Logic for Default Reasoning, Artificial Intelligence 13 (1980), 81–132.Google Scholar
  23. Sergot, M, Sadri, F, Kowalski, R, Kriwaczek, F, Hammond, P & Cory, H T, The British Nationality Act as a Logic Program, Communications of the ACM 29 (1986), 370–386.Google Scholar
  24. Tan, Y-H, Standard Inference in Partial Logic, Technical Report, Free University Amsterdam, 1989.Google Scholar
  25. Wagner, G, Logic Programming with Strong Negation and Inexact Predicates, Journal of Logic and Computation 1:6 (1991).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • David Pearce
    • 1
  1. 1.Gruppe Logik, Wissenstheorie und Information Institut für PhilosophieFreie Universität BerlinBerlin 33

Personalised recommendations