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.
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References
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.
M. Schmidt-Schauß. Computational Aspects of an Order-Sorted Logic with Term Declarations, volume 395 of LNAI. Springer-Verlag, 1989.
J.F. Sowa. Conceptual Structures, Information Processing in Mind and Machine. Addison Wesley, 1984.
M. Chein and M.L. Mugnier. Conceptual graphs, fundamental notions. RIA, 6.4:365–406, 1992.
H. v.d. Berg. Knowledge Graphs and Logic: One of two kinds. PhD thesis, Universiteit Twente, September 1993.
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.
R.M. Smullyan. First-Order Logic. Springer-Verlag, 1968.
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.
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.
M.L. Mugnier and M. Chein. Représenter des connaissances et raisonner avec des graphes. RIA, 10.1:7–56, 1996.
U. Reyle and D.M. Gabbay. Direct deductive computation on discourse representation structures. Linguistics and Philosophy, 17:343–390, 1994.
G. Kerdiles. Analytic tableaux for an extended language of conceptual graphs. RR LIRMM, 97002, 1997.
O. Haemmerle. CoGITo: une plate-forme de développement de logiciel sur les graphes conceptuels. PhD thesis, Université Montpellier II, France, January 1995.
A. Preller, M.L. Mugnier, and M. Chein. Logic for nested graphs. Computational Intelligence Journal, 95-02-558, 1995.
M.L. Mugnier and M. Chein. Quelques classes de graphes emboîtés équivalentes. RR LIRMM, 96063, 1996.
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© 1997 Springer-Verlag Berlin Heidelberg
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Kerdiles, G., Salvat, E. (1997). A sound and complete CG proof procedure combining projections with analytic tableaux. In: Lukose, D., Delugach, H., Keeler, M., Searle, L., Sowa, J. (eds) Conceptual Structures: Fulfilling Peirce's Dream. ICCS 1997. Lecture Notes in Computer Science, vol 1257. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0027884
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DOI: https://doi.org/10.1007/BFb0027884
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