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Exact knowledge compilation in predicate calculus: The partial achievement case

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Book cover Automated Deduction—CADE-14 (CADE 1997)

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Abstract

Forward chaining is an inference algorithm based on modus ponens which is widely used but unfortunately incomplete with respect to the usual boolean logic. A solution to this incompleteness is to compile the knowledge base so that forward chaining becomes complete for any base of facts. This compilation is called achievement and was so far restricted to propositional calculus. In this paper, we extend this compilation method to the predicate calculus. To our knowledge, this is the first exact knowledge compilation for first order logic.

This work is supported by the Conseil Régional Nord-Pas-de-Calais and the CNRS as part of the GANYMEDE II project

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References

  1. Chin-Liang Chang and Richard Char-Tung Lee, Symbolic logic and mechanical theorem proving, Academic Press, 1973.

    Google Scholar 

  2. Mukesh Dalal, Tractable Reasoning In Knowledge Representation Systems, Ph.D. thesis, Graduate School, New Brunswick, New Jersey, May 1995.

    Google Scholar 

  3. Alvaro del Val, Tractable databases: How to make propositional unit resolution complete through compilation, KR'94, Proceedings of Fourth International Conference on Principles of Knowledge Representation and Reasoning (J. Doyle, E. Sandewall, and P. Torassi, eds.), 1994, pp. 551–561.

    Google Scholar 

  4. Alvaro del Val, Approximate knowledge compilation: The first order case, AAAI'96, Proceedings of the Thirteenth National American Conference on Artificial Intelligence, 1996, pp. 498–503.

    Google Scholar 

  5. Kenneth D. Forbus and Johan de Kleer, Building Problem Solvers, MIT Press, 1993.

    Google Scholar 

  6. Katsumi Inoue, Studies on Abductive and Nonmonotonic Reasoning, Ph.D. thesis, Faculty of Engineering of Kyoto University, October 1992.

    Google Scholar 

  7. Henry Kautz and Bart Selman, Forming concepts for fast inference, Proceedings of the Tenth National Conference on Artificial Intelligence (AAAI'92) (San Jose, Calif.), MIT Press, Cambridge, Mass., 1992, pp. 786–793.

    Google Scholar 

  8. Donald W. Loveland, Automated Theorem Proving: A logical Basis, North Holland Publishing Company, Amsterdam, 1978.

    MATH  Google Scholar 

  9. Pierre Marquis, Knowledge Compilation Using Theory Prime Implicates, Proceedings of the Fourteenth International Joint Conference on Artificial Intelligence (IJCAI'95) (Montreal), 1995, pp. 837–843.

    Google Scholar 

  10. Philippe Mathieu, L'utilisation de la logique trivaluée dans les systèmes experts, Ph.D. thesis, Université des Sciences et Technologies de Lille, France, 1991.

    Google Scholar 

  11. Philippe Mathieu and Jean-Paul Delahaye, The logical compilation of knowledge bases, Proceedings of JELIA'90 (Amsterdam), Lecture Notes in Artificial Intelligence, vol. 478, Springer-Verlag, 1990, pp. 386–398.

    Google Scholar 

  12. Philippe Mathieu and Jean-Paul Delahaye, A kind of logical compilation for knowledge bases, Theoretical Computer Science 131 (1994), 197–218.

    Article  MathSciNet  Google Scholar 

  13. Bertrand Mazure and Pierre Marquis, Theory Reasoning within Implicant Cover Compilations, Proceedings of the ECAI'96 Workshop on Advances in Prepositional Deduction (Budapest), 1996, pp. 65–69.

    Google Scholar 

  14. Pierre Marquis and Samira Sadaoui, A New Algorithm for Computing Theory Prime Implicates Compilations, Proceedings of the Thirteenth National Conference on Artificial Intelligence (AAAI'96) (Portland (OR)), 1996, pp. 504–509.

    Google Scholar 

  15. Olivier Roussel and Philippe Mathieu, A New Method for Knowledge Compilation: the Achievement by Cycle Search, Proceedings of CADE-13 (New Brunswick, NJ, USA) (M.A. McRobbie and J.K. Slaney, eds.), Lecture Notes in Artificial Intelligence, vol. 1104, Springer-Verlag, 1996, pp. 493–507.

    Google Scholar 

  16. J. A. Robinson, A Machine-Oriented Logic Based on the Resolution Principle, Journal of the ACM 12 (1965), no. 1, 23–41.

    Article  MathSciNet  Google Scholar 

  17. Olivier Roussel, L'achèvement des bases de connaissances en calcul propositionnel et en calcul des prédicats, Ph.D. thesis, Université des Sciences et Technologies de Lille, France, Janvier 1997.

    Google Scholar 

  18. Olivier Roussel, The Achievement of Knowledge Bases in Propositional Calculus and in Predicate Calculus, Ph.D. thesis, Université des Sciences et Technologies de Lille, France, 1997, translation of [Rou97a] (in progress).

    Google Scholar 

  19. Robert Schrag, Compilation for Critically Constrained Knowledge Bases, Proceedings of the Thirteenth National Conference on Artificial Intelligence (AAAI'96) (Portland (OR)), 1996, pp. 510–515.

    Google Scholar 

  20. Pierre Siegel, Représentation et utilisation de la connaissance en calcul propositionnel, Ph.D. thesis, Université de Aix-Marseille II, Faculté des Sciences de Luminy, France, 1987, Thèse d'Etat.

    Google Scholar 

  21. Bart Selman and Henry Kautz, Knowledge compilation using Horn approximations, Proceedings of the Ninth National Conference on Artificial Intelligence (AAAI'91) (Anaheim, Calif.), MIT Press, Cambridge, Mass., 1991, pp. 904–909.

    Google Scholar 

  22. Bart Selman and Henry Kautz, Knowledge Compilation and Theory Approximation, Journal of the ACM 43 (1996), no. 2, 193–224.

    Article  MathSciNet  Google Scholar 

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William McCune

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© 1997 Springer-Verlag Berlin Heidelberg

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Roussel, O., Mathieu, P. (1997). Exact knowledge compilation in predicate calculus: The partial achievement case. In: McCune, W. (eds) Automated Deduction—CADE-14. CADE 1997. Lecture Notes in Computer Science, vol 1249. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63104-6_17

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  • DOI: https://doi.org/10.1007/3-540-63104-6_17

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  • Online ISBN: 978-3-540-69140-2

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