Abstract
The universal marker (i.e., universal quantifier) and the functional relation are two useful notations that make Conceptual Graph (CG) representations more concise in expressing universally quantified facts and functional dependencies, which are commonly used in knowledge bases, logic programs and data conceptual schemas. We introduce an expansion rule that formally defines the semantics of CGs containing universal markers and/or functional relations. On the basis of this formal semantics, we define two reasoning operations that are performed directly on CGs with these two notations to make them more useful. One operation is the universal CG projection defining the subsumption relation on the extended CGs. The other operation is the universal concept join performing universal instantiations and inheritances simultaneously in one graph operation. Both the operations are proved to be sound with respect to their described interpretations.
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References
ANSI (1993), IRDS Conceptual Schema. X3H4/93-196.
Creasy, P.N. & Ellis, G. (1993), A Conceptual Graphs Approach to Conceptual Schema Integration. In Mineau & Moulin & Sowa (eds): Conceptual Graphs for Knowledge Representation, LNAINo. 699, Springer-Verlag, pp. 126–141.
Ellis, G. & Lehmann, F. (1994), Exploiting the Induced Order on Type-Labelled Graphs for Fast Knowledge Retrieval. In Tepfenhart & Dick & Sowa (eds): Conceptual Structures: Current Practices, LNAI No. 835, Springer-Verlag, pp. 293–310.
Ghosh, B.C. (1996), Conceptual Graph Language — A Language of Logic and Information in Conceptual Structures. PhD Dissertation, Asian Institute of Technology.
Heaton, J.E. & Kocura, P. (1991), Negation and Projection of Conceptual Graphs. Proc. of the Sixth Annual Workshop on Conceptual Structures, 1991.
Lloyd, J.W. (1987), Foundations of Logic Programming. Springer-Verlag.
Mineau, G.W. (1994), Views, Mappings and Functions: Essential Definitions to The Conceptual Graph Theory. In Tepfenhart & Dick & Sowa (eds): Conceptual Structures: Current Practices, LNAINo. 835, Springer-Verlag, pp. 160–174.
Sowa, J.F. (1984), Conceptual Structures: Information Processing in Mind and Machine. Addison Wesley, Massachusetts.
Sowa, J.F. (1994), Knowledge Representation: Logical, Philosophical and Computational Foundations. A draft book in preparation.
Ullman, J.D. (1988), Principles of Database and Knowledge-Base Systems, Vol. 1. Computer Science Press, Rockville, Maryland.
Willems, M. (1995), Projection and Unification for Conceptual Graphs. In Ellis & Levinson & Rich & Sowa (eds): Conceptual Structures: Applications, Implementation and Theory, LNAI No. 954, Springer-Verlag, pp. 278–292.
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© 1997 Springer-Verlag Berlin Heidelberg
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Cao, T.H., Creasy, P.N. (1997). Universal marker and functional relation: Semantics and operations. 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/BFb0027887
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DOI: https://doi.org/10.1007/BFb0027887
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