Paraconsistent logic programming

  • Howard A. Blair
  • V. S. Subrahmanian
Session 6 Logic Programming
Part of the Lecture Notes in Computer Science book series (LNCS, volume 287)


This paper makes two contributions. Firstly, we give a semantics for sets of clauses of the form L0L1& ... &L n where each L i is a literal. We call such clauses generally-Horn clauses. Any such endeavour has to give a coherent, formal treatment of inconsistency (in the sense of two-valued logic). Thus, as a second contribution, we give a robust semantics for generally-Horn programs that allows us to “make sense” of sets of generally-Horn clauses that are inconsistent (in the two-valued logic sense). This applies to the design of very large knowledge bases where inconsistent information is often present.


Logic Program Logic Programming Operational Semantic Ground Atom Paraconsistent Logic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [AS87]
    Anand,R.,Subrahmanian,V.S.(1987) FLOG: A Logic programming system based on a six-valued logic, Proc. AAAI Intl. Symp. on Knowledge Engg., Madrid, Spain, April 1987.Google Scholar
  2. [ABW86]
    Apt,K.,Blair,H,Walker,A.(1986) Towards a theory of declarative knowledge, to appear.Google Scholar
  3. [AR79]
    Arruda,A.I.(1979) A Survey of paraconsistent logic, in Mathematical Logic in Latin America, (eds. Arruda,A.I., Chuaqui,R.,Da Costa,N.C.A.) Proc. 4th Latin American Symp. on Math. Logic, Santiago, Dec. 1978, pps. 1–41, D.Reidel.Google Scholar
  4. [BM86a]
    Barbuti,R., Martelli,M. (1986) Completeness of the SLDNF-resolution for a class of logic programs, Proc. Intl. Symp. on Logic Prog., London, Lecture Notes in Computer Science No.225, (ed.Shapiro,E.), pps 600–614.Google Scholar
  5. [BM86b]
    Barbuti,R., Martelli,M. (1986) Completeness of SLDNF-resolution for structured programs, submitted for publication.Google Scholar
  6. [BE77]
    Belnap,N.D. (1977) A Useful four-valued Logic, in Modern Uses of Many-valued Logic (eds. Epstein,G., Dunn,J.M.), pps. 8–37, D.Reidel.Google Scholar
  7. [BL86]
    Blair,H.A. (1986) Decidability in the Herbrand base, to appear.Google Scholar
  8. [BS87]
    Blair,H.A.,Subrahmanian,V.S. (1987) A Logical Framework for Approximate Reasoning in Logic programming, in preparation.Google Scholar
  9. [CA74]
    Costa, N.C.A.da (1974) On the theory of inconsistent formal systems, Notre Dame J. of Formal Logic 15, pps 497–510.Google Scholar
  10. [CA77]
    Costa, N.C.A.da, Alves, E.H. (1977) A semantical analysis of the calculi C n, Notre Dame J. of Formal Logic 18, pps 621–630.Google Scholar
  11. [CA81]
    Costa, N.C.A.da, Alves, H. (1981) Relations between paraconsistent logic and Many-valued logic, Bull. of the Section of Logic, 10, pps 185–191.Google Scholar
  12. [CA87]
    Costa,N.C.A.,Marconi,D. (1987) An Overview of Paraconsistent Logic in the 80's, to appear in Logica Nova, Akademie Verlag, Berlin.Google Scholar
  13. [FI85]
    Fitting, M. (1985) A Kripke-Kleene semantics for logic programming, J. of Logic Prog. 4, pps 295–312.Google Scholar
  14. [JLM86]
    Jaffar,J.,Lassez,J.-L.,Maher,M. (1986) Issues and trends in the Semantics of Logic Programming, Proc. 3rd Intl. Conf. on Logic Programming, Lecture Notes in Computer Sci., Vol. 225, Springer Verlag.Google Scholar
  15. [JS86]
    Jaffar, J., Stuckey, P.J. (1986) Canonical Logic Programs, J. of Logic Programming, 3,2, pps 143–155.CrossRefGoogle Scholar
  16. [K57]
    Kleene,S.C. (1957) Introduction to Metamathematics, Van Nostrand Reinhold.Google Scholar
  17. [LL84]
    Lloyd,J.W.(1984) Foundations of Logic Programming, Springer-Verlag.Google Scholar
  18. [LM85]
    Lassez, J.-L.,Maher, M.(1985) Optimal fixed points of logic programs, Theoret. Comput. Sci., 39, pps 115–125.CrossRefGoogle Scholar
  19. [NA86]
    Naish,L. (1986) Negation and quantifiers in NU-Prolog, Proc. 3rd Intl. Conf. on Logic Prog., London, Lecture Notes in Comp. Sci., Vol. 225, pps 624–634, Springer-Verlag.Google Scholar
  20. [PE86]
    Perlis, D. (1986) On the consistency of commonsense reasoning, Computational Intelligence, 2, pps 180–190.Google Scholar
  21. [PG86]
    Poole, D.,Goebel, R. (1986) Gracefully adding negation and disjunction in Prolog, Proc. 3rd Intl. Conf. on Logic Prog., London, Lecture Notes in Comp. Sci., Vol. 225, pps 635–641, Springer-Verlag.Google Scholar
  22. [S87a]
    Subrahmanian, V.S. (1987) On the semantics of quantitative logic programs, 4th IEEE Symp. on Logic Prog., San Francisco, Sep. 1987, (accepted-to appear).Google Scholar
  23. [S87b]
    Subrahmanian,V.S. (1987) Towards a theory of evidential reasoning in logic programming, Logic Colloquium '87 (European Summer Meeting of the Association of Symbolic Logic), Granada, Spain, July 1987 (accepted-to appear).Google Scholar
  24. [VE86]
    Van Emden, M. (1986) Quantitative deduction and its fixpoint theory, J. of Logic Prog., 4,1,pps 37–53.CrossRefGoogle Scholar
  25. [VI86]
    Visser, A. (1984) Four valued semantics and the liar, J. of Philosophical Logic, 13,pps 181–212.CrossRefGoogle Scholar
  26. [VK76]
    Van Emden, M., Kowalski, R. (1976) The semantics of predicate logic as a programming language, JACM, 23,4,pps 733–742.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Howard A. Blair
    • 1
  • V. S. Subrahmanian
    • 1
  1. 1.Logic Programming Theory Group School of Computer & Information ScienceSyracuse UniversitySyracuse

Personalised recommendations