Skip to main content

An Incremental Algorithm for Computing Prime Implicates in Modal Logic

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 8402)

Abstract

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.

Keywords

  • modal logic
  • prime implicates
  • knowledge compilation

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-319-06089-7_13
  • Chapter length: 15 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   79.99
Price excludes VAT (USA)
  • ISBN: 978-3-319-06089-7
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   99.99
Price excludes VAT (USA)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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. Bienvenu, M.: Consequence Finding in Modal Logic. PhD Thesis, Universit Paul Sabatier (May 7, 2009)

    Google Scholar 

  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. 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. 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. Darwiche, A., Marquis, P.: A knowledge compilation map. Journal of Artificial Intelligence Research 17, 229–264 (2002)

    MATH  MathSciNet  Google Scholar 

  7. Jackson, P., Pais, J.: Computing prime implicants. In: Stickel, M.E. (ed.) CADE 1990. LNCS, vol. 449, pp. 543–557. Springer, Heidelberg (1990)

    CrossRef  Google Scholar 

  8. Kean, A., Tsiknis, G.: An incremental method for generating prime implicants/implicates. J. Symb. Comput. 9(2), 185–206 (1990)

    CrossRef  MATH  MathSciNet  Google Scholar 

  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. 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. 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. Raut, M.K., Singh, A.: Prime implicates of first order formulas. IJCSA 1(1), 1–11 (2004)

    Google Scholar 

  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. Shiny, A.K., Pujari, A.K.: Computation of prime implicants using matrix and paths. J. Log. Comput. 8(2), 135–145 (1998)

    CrossRef  MATH  MathSciNet  Google Scholar 

  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)

    CrossRef  MathSciNet  Google Scholar 

  16. Strzemecki, T.: Polynomial-time algorithm for generation of prime implicants. Journal of Complexity 8, 37–63 (1992)

    CrossRef  MATH  MathSciNet  Google Scholar 

  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)

    CrossRef  Google Scholar 

  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)

    CrossRef  Google Scholar 

  19. Przymusinski, T.C.: An algorithm to compute circumscription. Artif. Intell. 38(1), 49–73 (1989)

    CrossRef  MATH  MathSciNet  Google Scholar 

  20. Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge University Press, Cambridge (2002)

    Google Scholar 

  21. Blackburn, P., van Benthem, J., Wolter, F.: Handbook of modal logic. Elsevier, Amsterdam (2007)

    MATH  Google Scholar 

  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. Raut, M.K.: An incremental knowledge compilation in first order logic. CoRR, abs/1110.6738 (2011)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Raut, M.K. (2014). An Incremental Algorithm for Computing Prime Implicates in Modal Logic. In: Gopal, T.V., Agrawal, M., Li, A., Cooper, S.B. (eds) Theory and Applications of Models of Computation. TAMC 2014. Lecture Notes in Computer Science, vol 8402. Springer, Cham. https://doi.org/10.1007/978-3-319-06089-7_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-06089-7_13

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-06088-0

  • Online ISBN: 978-3-319-06089-7

  • eBook Packages: Computer ScienceComputer Science (R0)