An Incremental Algorithm for Computing Prime Implicates in Modal Logic

  • Manoj K. Raut
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8402)


The algorithm to compute prime implicates and prime implicants in modal logic \({\mathcal{K}}\) has been suggested in [1]. In this paper we suggest an incremental algorithm to compute the prime implicates of a knowledge base KB and a new knowledge base F from Π(KB) ∧ F in modal logic \({\mathcal{K}}\), where Π(KB) is the set of prime implicates of KB and we also prove the correctness of the algorithm.


modal logic prime implicates knowledge compilation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bienvenu, M.: Prime implicates and prime implicants: From propositional to modal logic. J. Artif. Intell. Res. (JAIR) 36, 71–128 (2009)Google Scholar
  2. 2.
    Bienvenu, M.: Consequence Finding in Modal Logic. PhD Thesis, Universit Paul Sabatier (May 7, 2009)Google Scholar
  3. 3.
    Cook, S.A.: The complexity of theorem-proving procedures. In: Proc. 3rd ACM Symp. on the Theory of Computing, pp. 151–158. ACM Press (1971)Google Scholar
  4. 4.
    Cadoli, M., Donini, F.M.: A survey on knowledge compilation. AI Communications-The European Journal for Articial Intelligence 10, 137–150 (1998)Google Scholar
  5. 5.
    Coudert, O., Madre, J.: Implicit and incremental computation of primes and essential primes of boolean functions. In: Proceedings of the 29th ACM/IEEE Design Automation Conference, pp. 36–39. IEEE Computer Society Press (1991)Google Scholar
  6. 6.
    Darwiche, A., Marquis, P.: A knowledge compilation map. Journal of Artificial Intelligence Research 17, 229–264 (2002)zbMATHMathSciNetGoogle Scholar
  7. 7.
    Jackson, P., Pais, J.: Computing prime implicants. In: Stickel, M.E. (ed.) CADE 1990. LNCS, vol. 449, pp. 543–557. Springer, Heidelberg (1990)CrossRefGoogle Scholar
  8. 8.
    Kean, A., Tsiknis, G.: An incremental method for generating prime implicants/implicates. J. Symb. Comput. 9(2), 185–206 (1990)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    de Kleer, J.: An assumption-based tms. In: Ginsberg, M.L. (ed.) Readings in Nonmonotonic Reasoning, pp. 280–297. Kaufmann, Los Altos (1987)Google Scholar
  10. 10.
    de Kleer, J.: An improved incremental algorithm for generating prime implicates. In: Proceedings of the Tenth National Conference on Artificial Intelligence, AAAI 1992, pp. 780–785. AAAI Press (1992)Google Scholar
  11. 11.
    Ngair, T.H.: A new algorithm for incremental prime implicate generation. In: Proc. of the 13th IJCAI, Chambery, France, pp. 46–51 (1993)Google Scholar
  12. 12.
    Raut, M.K., Singh, A.: Prime implicates of first order formulas. IJCSA 1(1), 1–11 (2004)Google Scholar
  13. 13.
    Reiter, R., de Kleer, J.: Foundations of assumption-based truth maintenance systems. In: Proceedings of the Sixth National Conference on Artificial Intelligence (AAAI 1987), pp. 183–188 (1987)Google Scholar
  14. 14.
    Shiny, A.K., Pujari, A.K.: Computation of prime implicants using matrix and paths. J. Log. Comput. 8(2), 135–145 (1998)CrossRefzbMATHMathSciNetGoogle Scholar
  15. 15.
    Slagle, J.R., Chang, C.L., Lee, R.C.T.: A new algorithm for generating prime implicants. IEEE Trans. on Comp. C-19(4), 304–310 (1970)CrossRefMathSciNetGoogle Scholar
  16. 16.
    Strzemecki, T.: Polynomial-time algorithm for generation of prime implicants. Journal of Complexity 8, 37–63 (1992)CrossRefzbMATHMathSciNetGoogle Scholar
  17. 17.
    Tison, P.: Generalized consensus theory and application to the minimisation of boolean functions. IEEE Trans. on Elec. Comp. EC-16(4), 446–456 (1967)CrossRefGoogle Scholar
  18. 18.
    Pagnucco, M.: Knowledge compilation for belief change. In: Sattar, A., Kang, B.-H. (eds.) AI 2006. LNCS (LNAI), vol. 4304, pp. 90–99. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  19. 19.
    Przymusinski, T.C.: An algorithm to compute circumscription. Artif. Intell. 38(1), 49–73 (1989)CrossRefzbMATHMathSciNetGoogle Scholar
  20. 20.
    Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge University Press, Cambridge (2002)Google Scholar
  21. 21.
    Blackburn, P., van Benthem, J., Wolter, F.: Handbook of modal logic. Elsevier, Amsterdam (2007)zbMATHGoogle Scholar
  22. 22.
    Jackson, P.: Computing prime implicants incrementally. In: Proceedings of the 11th International Conference on Automated Deduction, vol. 607, pp. 253–267 (1992)Google Scholar
  23. 23.
    Raut, M.K.: An incremental knowledge compilation in first order logic. CoRR, abs/1110.6738 (2011)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Manoj K. Raut
    • 1
  1. 1.Dhirubhai Ambani Institute of Information and Communication TechnologyGandhinagarIndia

Personalised recommendations