A sound and complete CG proof procedure combining projections with analytic tableaux

  • Gwen Kerdiles
  • Eric Salvat
Formal Reasoning
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1257)

Abstract

Conceptual Graphs offer an attractive and intuitive formalism for knowledge representation in Artificial Intelligence. The formalism calls for efficient systems of reasoning. Projection is one such tool for a language limited to conjunction and existential quantification (Simple Conceptual Graphs). Projection is very efficient for certain classes of Conceptual Graphs and offers an original approach to deduction: the perspective of graph matching. The aim of this paper is twofold: Propose an efficient analytic deduction system that combines analytic tableaux with projection for a language of Conceptual Graphs extended to all non functional First-Order Logic formulae and compare this method with the one introduced in [1] for Simple Conceptual Graph rules.

Keywords

Variable Marker Individual Marker Connection Point Conceptual Graph Concept Node 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References

  1. 1.
    E. Salvat and M.L. Mugnier. Sound and complete forward and backward chaining of graph rules. In proceedings of ICCS'96, volume 1115 of LNAI, pages 248–262. Springer-Verlag, 1996.Google Scholar
  2. 2.
    M. Schmidt-Schauß. Computational Aspects of an Order-Sorted Logic with Term Declarations, volume 395 of LNAI. Springer-Verlag, 1989.Google Scholar
  3. 3.
    J.F. Sowa. Conceptual Structures, Information Processing in Mind and Machine. Addison Wesley, 1984.Google Scholar
  4. 4.
    M. Chein and M.L. Mugnier. Conceptual graphs, fundamental notions. RIA, 6.4:365–406, 1992.Google Scholar
  5. 5.
    H. v.d. Berg. Knowledge Graphs and Logic: One of two kinds. PhD thesis, Universiteit Twente, September 1993.Google Scholar
  6. 6.
    M. Wermelinger. Conceptual graphs and first-order logic. In proceedings of ICCS'95, Santa Cruz, USA, volume 954 of LNAI, pages 323–337. Springer-Verlag, 1995.Google Scholar
  7. 7.
    R.M. Smullyan. First-Order Logic. Springer-Verlag, 1968.Google Scholar
  8. 8.
    P.H. Schmitt and W. Wernecke. Tableau calculus for order sorted logic. In Sorts and Types in Artificial Intelligence, volume 418 of LNAI, pages 49–60. Springer-Verlag, 1990.Google Scholar
  9. 9.
    B.C. Ghosh. Conceptual Graph Language: A Language of Logic and Information in Conceptual Structures. PhD thesis, Asian Institute of Technology, Bangkok, Thailand, February 1996.Google Scholar
  10. 10.
    M.L. Mugnier and M. Chein. Représenter des connaissances et raisonner avec des graphes. RIA, 10.1:7–56, 1996.Google Scholar
  11. 11.
    U. Reyle and D.M. Gabbay. Direct deductive computation on discourse representation structures. Linguistics and Philosophy, 17:343–390, 1994.Google Scholar
  12. 12.
    G. Kerdiles. Analytic tableaux for an extended language of conceptual graphs. RR LIRMM, 97002, 1997.Google Scholar
  13. 13.
    O. Haemmerle. CoGITo: une plate-forme de développement de logiciel sur les graphes conceptuels. PhD thesis, Université Montpellier II, France, January 1995.Google Scholar
  14. 14.
    A. Preller, M.L. Mugnier, and M. Chein. Logic for nested graphs. Computational Intelligence Journal, 95-02-558, 1995.Google Scholar
  15. 15.
    M.L. Mugnier and M. Chein. Quelques classes de graphes emboîtés équivalentes. RR LIRMM, 96063, 1996.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Gwen Kerdiles
    • 1
  • Eric Salvat
    • 1
  1. 1.L.I.R.M.M.U.M.R. 9928 Université Montpellier II/C.N.R.S.Montpellier cedex 5France

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