Skip to main content
SpringerLink
Log in

Tableaux, Path Dissolution, and Decomposable Negation Normal Form for Knowledge Compilation

  • Conference paper
Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX 2003)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2796))

Abstract

Decomposable negation normal form (DNNF) was developed primarily for knowledge compilation. Formulas in DNNF are linkless, in negation normal form (NNF), and have the property that atoms are not shared across conjunctions. Full dissolvents are linkless NNF formulas that do not in general have the latter property. However, many of the applications of DNNF can be obtained with full dissolvents. Two additional methods — regular tableaux and semantic factoring — are shown to produce equivalent DNNF. A class of formulae is presented on which earlier DNNF conversion techniques are necessarily exponential; path dissolution and semantic factoring handle these formulae in linear time.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bryant, R.E.: Symbolic Boolean manipulation with ordered binary decision diagrams. ACM Computing Surveys 24(3), 293–318 (1992)

    Article  Google Scholar 

  2. Cadoli, M., Donini, F.M.: A survey on knowledge compilation. AI Communications 10, 137–150 (1997)

    Google Scholar 

  3. D’Agostino, M., Gabbay, D.M., Hähnle, R., Posegga, J.: Handbook of Tableau Methods. Kluwer Academic Publishers, Dordrecht (1999)

    Google Scholar 

  4. Darwiche, A.: Compiling devices: A structure-based approach. In: Proc. International Conference on Principles of Knowledge Representation and Reasoning (KR 1998), pp. 156–166. Morgan-Kaufmann, San Francisco (1998)

    Google Scholar 

  5. Darwiche, A.: Model based diagnosis using structured system descriptions. Journal of A. I. Research 8, 165–222

    Google Scholar 

  6. Darwiche, A.: Decomposable negation normal form. J.ACM 48(4), 608–647 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  7. Darwiche, A., Marquis, P.: A knowledge compilation map. J. of AI Research 17, 229–264 (2002)

    MATH  MathSciNet  Google Scholar 

  8. Davis, M., Putnam, H.: A computing procedure for quantification theory. J.ACM 7, 201–215 (1960)

    Article  MATH  MathSciNet  Google Scholar 

  9. Fitting, M.: First-Order Logic and Automated Theorem Proving, 2nd edn. Springer, New York (1996)

    MATH  Google Scholar 

  10. Forbus, K.D., de Kleer, J.: Building Problem Solvers. MIT Press, Cambridge (1993)

    MATH  Google Scholar 

  11. Goubault, J., Posegga, J.: BDD’s and automated deduction. In: Raś, Z.W., Zemankova, M. (eds.) ISMIS 1994. LNCS (LNAI), vol. 869, pp. 541–550. Springer, Heidelberg (1994)

    Google Scholar 

  12. Letz, R.: First-order calculi and proof procedures for automated deduction, Ph.D. dissertation, TU Darmstadt (1993)

    Google Scholar 

  13. Letz, R., Mayr, K., Goller, C.: Controlled integration of the cut rule into connection tableau calculi. Journal of Automated Reasoning 13(3), 297–338 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  14. Marquis, P.: Knowledge compilation using theory prime implicates. In: Proc. International Joint Conference on Artificial Intelligence (IJCAI), pp. 837–843. Morgan- Kaufmann, San Mateo (1995)

    Google Scholar 

  15. Murray, N.V., Ramesh, A.: An application of non-clausal deduction in diagnosis. In: Proceedings of the Eighth International Symposium on Artificial Intelligence, Monterrey, Mexico, October 17-20, pp. 378–385 (1995)

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  17. Murray, N.V., Rosenthal, E.: Reexamining tractability of analytic tableaux. In: Proc. of the 1990 Symposium on Symbolic and Algebraic Computation, pp. 52–59 (1990)

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  19. Murray, N.V., Rosenthal, E.: On the relative merits of path dissolution and the method of analytic tableaux. Theoretical Computer Science 131, 1–28 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  20. Prawitz, D.: A proof procedure with matrix reduction. Lecture Notes in Mathematics, vol. 125, pp. 207–213. Springer, Heidelberg (1970)

    Google Scholar 

  21. Ramesh, A., Beckert, B., Hähnle, R., Murray, N.V.: Fast subsumption checks using anti-links. Journal of Automated Reasoning 18(1), 47–83 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  22. Ramesh, A., Becker, G., Murray, N.V.: CNF and DNF considered harmful for computing prime implicants/implicates. Journal of Automated Reasoning 18(3), 337–356 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  23. Ramesh, A., Murray, N.V.: An application of non-clausal deduction in diagnosis. Expert Systems with Applications 12(1), 119–126 (1997)

    Article  MathSciNet  Google Scholar 

  24. Selman, B., Kautz, H.: Knowledge compilation and theory approximation. J.ACM 43(2), 193–224 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  25. Smullyan, R.M.: First-Order Logic, 2nd edn. Dover Press, New York (1995)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, State University of New York, Albany, NY, 12222, USA

    Neil V. Murray

  2. Department of Mathematics, University of New Haven, West Haven, CT, 06516, USA

    Erik Rosenthal

Authors
  1. Neil V. Murray
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Erik Rosenthal
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dipartimento di Informatica e Automazione, Università di Roma Tre, via Vasca Navale 79, 00146, Roma, Italia

    Marta Cialdea Mayer

  2. Dipartimento di Informatica e Sistemistica (DIS), Sapienza, University of Rome “Sapienza”, via Ariosto 25, 00185, Roma

    Fiora Pirri

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Murray, N.V., Rosenthal, E. (2003). Tableaux, Path Dissolution, and Decomposable Negation Normal Form for Knowledge Compilation. In: Cialdea Mayer, M., Pirri, F. (eds) Automated Reasoning with Analytic Tableaux and Related Methods . TABLEAUX 2003. Lecture Notes in Computer Science(), vol 2796. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45206-5_14

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-45206-5_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40787-4

  • Online ISBN: 978-3-540-45206-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation