Skip to main content
SpringerLink
Log in

Projection: A unification procedure for tableaux in Conceptual Graphs

  • Contributed Papers
  • Conference paper
  • First Online:
Book cover Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX 1997)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1227))

Abstract

Conceptual Graphs offer a formalism for knowledge representation in Artificial Intelligence, inspired by both order-sorted logic and Peirce's Existential Graphs. These graphical structures provide an attractive and intuitive representation of information and are particularly suitable for human-machine interfaces. Conceptual Graphs borrow from order-sorted logic the notion of sort. Sorting not only provides an intuitive classification of objects of the language, but also an efficient way of restricting search spaces (for example, in unification).

The formalism calls for efficient systems of reasoning in order to compete with logical programming. 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: enrich the language of Simple Conceptual Graphs with implication and negation, and propose an efficient analytic deduction system that combines analytic tableaux with projection.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. H. v.d. Berg. Knowledge Graphs and Logic: One of two kinds. PhD thesis, Universiteit Twente, September 1993.

    Google Scholar 

  2. K.H. Bläsius, U. Hedtstück, and C.-R. Rollinger, editors. Sorts and Types in Artificial Intelligence, volume 418 of LNAI. Springer-Verlag, 1990. Proceedings of Workshop Eringerfeld, FRG, April 1989.

    Google Scholar 

  3. M. Baaz and A. Leitsch. On Skolemization and Proof Complexity. Fundamenta Informaticae, 20:353–379, 1994.

    Google Scholar 

  4. M. Chein and M.L. Mugnier. Conceptual Graphs, Fundamental Notions. RIA, 6.4:365–406, 1992.

    Google Scholar 

  5. 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 

  6. G. Kerdiles. Analytic Tableaux for an extended language of Conceptual Graphs. RR LIRMM, 97002, 1997.

    Google Scholar 

  7. R. Manthey and F. Bry. SATCHMO: a theorem prover implemented in Prolog. LNCS, 310:415–434, 1988. CADE 9.

    Google Scholar 

  8. M.L. Mugnier and M. Chein. Polynomial algorithms for projection and matching. In Proceedings of the 7th Workshop on Conceptual Graphs, 1992. New Mexico State University, Las Cruces, New Mexico.

    Google Scholar 

  9. A. Preller, M.L. Mugnier, and M. Chein. Logic for Nested Graphs. Computational Intelligence Journal, 95-02-558, 1995.

    Google Scholar 

  10. U. Reyle and D.M. Gabbay. Direct Deductive Computation on Discourse Representation Structures. Linguistics and Philosophy, 17:343–390, August 1994.

    Google Scholar 

  11. 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 

  12. R.M. Smullyan. First-Order Logic. Springer-Verlag, 1968.

    Google Scholar 

  13. J.F. Sowa. Conceptual Structures, Information Processing in Mind and Machine. Addison Wesley, 1984.

    Google Scholar 

  14. M. Schmidt-Schauß. Computational Aspects of an Order-Sorted Logic with Term Declarations, volume 395 of LNAI. Springer-Verlag, Edited by J.Siekmann, 1989.

    Google Scholar 

  15. 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 

  16. 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 

Download references

Author information

Authors and Affiliations

  1. Faculty of Philosophy, University of Amsterdam, The Netherlands

    Gwen Kerdiles

  2. LIRMM, University of Montpellier, 161 Rue Ada, 34392, Montpellier Cedex 5, France

    Gwen Kerdiles

Authors
  1. Gwen Kerdiles
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Didier Galmiche

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kerdiles, G. (1997). Projection: A unification procedure for tableaux in Conceptual Graphs. In: Galmiche, D. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 1997. Lecture Notes in Computer Science, vol 1227. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0027416

Download citation

  • DOI: https://doi.org/10.1007/BFb0027416

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62920-7

  • Online ISBN: 978-3-540-69046-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation