Skip to main content

On anti-links

  • Conference paper
  • First Online:
Logic Programming and Automated Reasoning (LPAR 1994)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 822))

  • 126 Accesses

Abstract

The concept of anti-link is defined, and useful equivalence-preserving operations on propositional formulas based on anti-links are introduced. These operations eliminate a potentially large number of subsumed paths in a negation normal form formula. The operations have linear time complexity in the size of that part of the formula containing the anti-link.

These operations are useful for prime implicant/implicate algorithms because most of the computational effort in such algorithms is spent on subsumption checks.

This research was supported in part by National Science Foundation Grant CCR-9101208 (Ramesh and Murray) and by Deutsche Forschungsgemeinschaft within the Schwerpunktprogramm Deduktion (Hähnle and Beckert).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. de Kleer, J. An improved incremental algorithm for computing prime implicants. Proceedings of AAAI-92, 780–785.

    Google Scholar 

  2. Jackson, P., and Pais, J. Computing prime implicants. Proceedings of CADE-10, Kaiserslautern, W. Germany, July, 1990. In LNAI, Springer-Verlag, Vol. 449, 543–557.

    Google Scholar 

  3. Jackson, P. Computing prime implicants incrementally. Proceedings of CADE-11, Saratoga Springs, NY, June, 1992. In LNAI, Springer-Verlag, Vol. 607, 253–267.

    Google Scholar 

  4. Kean, A., and Tsiknis, G. An incremental method for generating prime implicants/implicates. Journal of Symbolic Computation 9 (1990), 185–206.

    Google Scholar 

  5. Kean, A., and Tsiknis, G. Assumption based reasoning and clause management systems. Computational Intelligence 8, 1 (Nov. 1992), 1–24.

    Google Scholar 

  6. Letz, R. First-order calculi and proof procedures for automated deduction. Ph.D. thesis, TH Darmstadt, June 1993.

    Google Scholar 

  7. Murray, N.V., and Rosenthal, E. Inference with path resolution and semantic graphs. J.ACM 34, 2 (April 1987), 225–254.

    Google Scholar 

  8. Murray, N.V., and Rosenthal, E. Path dissolution: A strongly complete rule of inference. Proceedings of AAAI-87, Seattle, WA, July 12–17, 1987, 161–166.

    Google Scholar 

  9. Murray, N.V., and Rosenthal, E. Dissolution: Making paths vanish. J.ACM 40, 3 (July 1993), 504–535.

    Google Scholar 

  10. Ngair,T. A new algorithm for incremental prime implicate generation. Proceedings of IJCAI-93, Chambery, France, August, 1993.

    Google Scholar 

  11. Przymusinski, T.C. An algorithm to compute circumscription. Artificial Intelligence 38 (1989), 49–73.

    Google Scholar 

  12. Ramesh, A., and Murray, N.V. Non-clausal deductive techniques for computing prime implicants and prime implicates. Proceedings of LPAR-93. St. Petersburg, Russia, July 13–20, 1993. In LNAI, Springer-Verlag, Vol. 698, 277–288.

    Google Scholar 

  13. Reiter, R. and de Kleer, J. Foundations of assumption-based truth maintenance systems: preliminary report. Proceedings of AAAI-87, Seattle, WA, July 12–17, 1987, 183–188.

    Google Scholar 

  14. Slagle, J.R., Chang, C.L., and Lee, R.C.T. A new algorithm for generating prime implicants. IEEE Transactions on Computers, C-19(4) (1970), 304–310.

    Google Scholar 

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

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Frank Pfenning

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Beckert, B., Hähnle, R., Ramesh, A., Murray, N.V. (1994). On anti-links. In: Pfenning, F. (eds) Logic Programming and Automated Reasoning. LPAR 1994. Lecture Notes in Computer Science, vol 822. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58216-9_44

Download citation

  • DOI: https://doi.org/10.1007/3-540-58216-9_44

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58216-8

  • Online ISBN: 978-3-540-48573-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics