The logical compilation of knowledge bases

  • Philippe Mathieu
  • Jean-Paul Delahaye
Selected Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 478)


Forward chaining cannot compute the two-valued consequence literals of a knowledge base (i.e. set of rules) with negations. If the user wants to compute them, he must use a particular algorithm which often takes a lot of time. We propose a compilation system of knowledge bases what we call logical compilation, which allows us to compute the two-valued consequence literals of a knowledge base (i.e. set of rules) using a forward chaining on the compiled base with any extensional knowledge base (i.e. set of basic facts added to knowledge base). Then we present several methods with their benefits to make this compilation. Finally we use this compilation in a wide propositional calculus and solve the ‘or’ problem in rule conclusion.


Expert system forward chaining knowledge representation three-valued logic 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

9. References

  1. [ABW 88]
    K.R. Apt, H. Blair, A. Walker. Towards a Theory of Declarative Knowledge. Foundations of deductive databases and logic programming (J.Minker ed), Morgan Kaufmann, 1988, p 89–148.Google Scholar
  2. [Bib 81]
    W. Bibel. On Matrices with Connections. J of A.C.M. Vol 28, no4, 1981, p633–645.Google Scholar
  3. [Car 66]
    L. Caroll. La logique sans peine. Ed Hermann, 1966.Google Scholar
  4. [C&L]
    C.L.Chang and R.C.T. Lee. Symbolic Logic and Mechanical Theorem Proving. Academic Press, inc. 1973.Google Scholar
  5. [Del 87a]
    J.P. Delahaye. Forward chaining and computation of two-valued and three-valued models. 7th Int. Conf. on Expert Systems and Applications, Avignon 87. p1341–1360.Google Scholar
  6. [Del 87b]
    J.P. Delahaye. Semantics and Completeness of Forward Chaining in Propositionnal Calculus (in French). Research report IT no115, Laboratoire d'Informatique Fondamentale de Lille, 1987.Google Scholar
  7. [DM 89]
    J.P. Delahaye et P. Mathieu. The Achievement Notion and its Application to Rule Interpreters (in French). Research report IT no172, Laboratorie d'Informatique Fondamentale de Lille, september 89.Google Scholar
  8. [DM 90a]
    J.P. Delahaye et P. Mathieu. How to Make a Complete Computation with Forward Chaining?. Proceedings of IASTED 90, Honolulu, 1990.Google Scholar
  9. [DM 90b]
    J.P. Delahaye et P. Mathieu. For which bases forward chaining is sufficient?. Proceedings of Cognitiva 90, Madrid, 1990 (to appear).Google Scholar
  10. [DP 60]
    M. Davis, H. Putnam. A Computing Procedure for Quantification Theory. JACM 7, p201–215, 1960.Google Scholar
  11. [DT 90]
    J.P. Delahaye, V. Thibau. Programming in Three-Valued Logic, TCS (to appear), 1990.Google Scholar
  12. [Fit 85]
    M. Fitting. A Kripke-Kleene semantics for logic programs, J. of Logic Programming, vol 2, 1985, p295,312.Google Scholar
  13. [Fit 87]
    M. Fitting, M. Ben-Jacob. Stratified and Three-valued Logic Programming Semantics. Proc. 5th International Conference and Symposium in Logic Programming (Edited by Kowalski and Bowen), 1988, p.1054–1069.Google Scholar
  14. [Kle 52]
    S.C. Kleene. Introduction to metamathematics. Van Nostrand, New-York, 1952.Google Scholar
  15. [Kun 87]
    K. Kunen. Negation in Logic Programming. Journal of Logic Programming, vol 4, 1987, p289–308.Google Scholar
  16. [Kun 89]
    K. Kunen. Signed Data Dependencies in Logic Programs. Journal of Logic Programming, vol 7, 1989, p231–245.Google Scholar
  17. [Lee 67]
    C.T. Lee. A Completeness Theorem and a Computer Program for Finding Theorems Derivable from Given Axioms. Ph.D. Thesis, University of California, Berkeley, 1967.Google Scholar
  18. [Luk 63]
    J. Lukasiewicz. Elements of Mathematical Logic. Pergamon Press, 1963.Google Scholar
  19. [Prz 89]
    T. Przymusinski. Non-Monotonic Formalisms and Logic Programming. Proc. 6th Int. Conference on Logic Programming, Levi and Martelli eds, 1989, p655–674.Google Scholar
  20. [Rau 89]
    A. Rausy. L'Evaluation Sémantique en Calcul Propositionnel. Ph.D. Thesis GIA Marseille Luminy, 1989.Google Scholar
  21. [Sie 87]
    P. Siegel. Representation et utilisation de la connaissance en calcul propositionnel. Thèse d'état-GIA Marseille Luminy, 1987.Google Scholar
  22. [She 88]
    J.C. Shepherdson. Negation in logic programming. Foundations of deductive databases and logic programming (J.Minker ed), Morgan Kaufmann, 1988, p19–88.Google Scholar
  23. [Tur 84]
    R. Turner. Logics for Artificial Intelligence. Ellis Horwood, 1984.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Philippe Mathieu
    • 1
  • Jean-Paul Delahaye
    • 1
  1. 1.Laboratoire d'Informatique Fondamentale de Lille U.R.A. 369 CNRSUniversité des Sciences et Techniques de Lille Flandres ArtoisVilleneuve d'Ascq CedexFrance

Personalised recommendations