Abstract
It is well-known that problems like validity and subsumption of general CGs are undecidable, whereas subsumption is NP-complete for simple conceptual graphs (SGs) and tractable for SGs that are trees. We will employ results on decidable fragments of first-order logic to identify a natural and expressive fragment of CGs for which validity and subsumption is decidable in EXPTIME. In addition, we will extend existing work on the connection between SGs and description logics (DLs) by identifying a DL that corresponds to the class of SGs that are trees. This yields a tractability result previously unknown in the DL community.
This work was partially supported by the Deutsche Forschungsgemeinschaft Grant No. GRK 185/3-98 and Project No. GR 1324/3-1
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References
H. Andréka, J. van Benthem, and I. Németi. Modal languages and bounded fragments of predicate logic. J. of Philosophical Logic, 27(3):217–274, 1998.
F. Baader, R. Molitor, and S. Tobies. The Guarded Fragment of Conceptual Graphs. LTCS-Report 98–10, available at http://www-lti.informatik.rwth-aachen.de/Forschung/Papers.html.
F. Baader, R. Molitor, and S. Tobies. On the Relationship between Descripion Logics and Conceptual Graphs. LTCS-Report 98–11, available at http://www-lti.informatik.rwth-aachen.de/Forschung/Papers.html.
E. Börger, E. Grädel, and Y. Gurevich. The Classical Decision Problem. Perspectives in Mathematical Logic. Springer, 1997.
M. Chein and M. L. Mugnier. Conceptual graphs: fundamental notions. Revue d’Intelligence Artificielle, 6(4):365–406, 1992.
M. Chein, M. L. Mugnier, and G. Simonet. Nested graphs: a graph-based knowledge representation model with FOL semantics. In Proc. KR’98, 1998.
P. Coupey and C. Faron. Towards correspondences between conceptual graphs and description logics. In Proc. ICCS’98, LNCS 1453, 1998.
H. de Nivelle. A resolution decision procedure for the guarded fragment. In Proc. CADE-15, LNCS 1421, 1998.
F. M. Donini, M. Lenzerini, D. Nardi, and W. Nutt. The complexity of concept languages. Information and Computation, 134(1):1–58, 1997.
F. M. Donini, M. Lenzerini, D. Nardi, and A. Schaerf. Reasoning in description logics. In Foundation of Knowledge Representation, CSLI-Publications, 1996.
E. Grädel. On the restraining power of guards. Journal of Symbolic Logic, 1999. To appear.
G. Kerdiles and E. Salvat. A sound and complete CG proof procedure combining projections with analytic tableaux. In Proc. ICCS’97, LNCS 1257, 1997.
M. L. Mugnier and M. Chein. Polynomial algorithms for projection and matching. In Proc. 7th Workshop on Conceptual Structures, 1992, LNCS 754, 1993.
John F. Sowa. Conceptual Structures. Addison-Wesley, 1984.
J. van Benthem. Dynamic Bits and Pieces. Technical Report LP-1997-01, ILLC, University of Amsterdam, The Netherlands, 1997.
M. Wermelinger. Conceptual graphs and first-order logic. In Proc. ICCS’95, LNCS 954, 1995.
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Baader, F., Molitor, R., Tobies, S. (1999). Tractable and Decidable Fragments of Conceptual Graphs. In: Tepfenhart, W.M., Cyre, W. (eds) Conceptual Structures: Standards and Practices. ICCS 1999. Lecture Notes in Computer Science(), vol 1640. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48659-3_31
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DOI: https://doi.org/10.1007/3-540-48659-3_31
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