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Duality in Knowledge Compilation Techniques

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Foundations of Intelligent Systems (ISMIS 2005)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3488))

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Abstract

Several classes of propositional formulas have been used as target languages for knowledge compilation. Some are based primarily on c-paths (essentially, the clauses in disjunctive normal form); others are based primarily on d-paths. Such duality is not surprising in light of the duality fundamental to classical logic. There is also duality among target languages in terms of how they treat links (complementary pairs of literals): Some are link-free; others are pairwise-linked (essentially, each pair of clauses is linked). In this paper, both types of duality are explored, first, by investigating the structure of existing forms, and secondly, by developing new forms for target languages.

This research was supported in part by the National Science Foundation under grant CCR-0229339.

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References

  1. Bibel, W.: Tautology testing with a generalized matrix method. Theoretical Computer Science 8, 31–44 (1979)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

  4. Chatalic, P., Simon, L.: Zres: The old Davis-Putnam procedure meets ZBDDs. In: McAllester, D. (ed.) CADE 2000. LNCS (LNAI), vol. 1831, pp. 449–454. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  5. 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 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  9. Hähnle, R., Murray, N.V., Rosenthal, E.: Normal forms for knowledge compilation. In: Hacid, M.-S., Murray, N.V., Raś, Z.W., Tsumoto, S. (eds.) ISMIS 2005. LNCS (LNAI), vol. 3488, pp. 304–313. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  10. Hai, L., Jigui, S.: Knowledge compilation using the extension rule. J. Automated Reasoning 32(2), 93–102 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  11. Henocque, L.: The prime normal form of boolean formulas (Submitted), Preliminary version available as a technical report at http://www.Isis.org/fiche.php?id=74&page=

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

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  14. 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 

  15. Murray, N.V., Rosenthal, E.: Tableaux, path dissolution, and decomposable negation normal form for knowledge compilation. In: Cialdea Mayer, M., Pirri, F. (eds.) TABLEAUX 2003. LNCS (LNAI), vol. 2796, pp. 165–180. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  16. Murray, N.V., Rosenthal, E.: Knowledge compilation and duality, Technical Report SUNYA-CS-04-07, Dept of Computer Science, SUNY Albany (October 2004)

    Google Scholar 

  17. Nelson, R.J.: Simplest normal truth functions. J. of Symbolic Logic 20, 105–108 (1955)

    Article  MATH  Google Scholar 

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

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  20. 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 

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

    Article  MATH  MathSciNet  Google Scholar 

  22. Walsh, T.: Non-clausal reasoning. In: Workshop on Disproving Non-Theorems, Non-Validity, and Non-Provability, IJCAR, Cork, Ireland (2004)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, State University of NewYork, 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
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  2. Erik Rosenthal
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Editor information

Editors and Affiliations

  1. LIRIS - UFR d’Informatique, Université Claude Bernard Lyon 1, 43, boulevard du 11 novembre 1918, 69622, Villeurbanne, France

    Mohand-Said Hacid

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

    Neil V. Murray

  3. Department of Computer Science, University of North Carolina, 28223, Charlotte, NC, USA

    Zbigniew W. Raś

  4. Shimane University, 89-1 Enya-cho Izumo, 6938501, Shimane, Japan

    Shusaku Tsumoto

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© 2005 Springer-Verlag Berlin Heidelberg

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Murray, N.V., Rosenthal, E. (2005). Duality in Knowledge Compilation Techniques. In: Hacid, MS., Murray, N.V., Raś, Z.W., Tsumoto, S. (eds) Foundations of Intelligent Systems. ISMIS 2005. Lecture Notes in Computer Science(), vol 3488. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11425274_19

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  • DOI: https://doi.org/10.1007/11425274_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25878-0

  • Online ISBN: 978-3-540-31949-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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