Abstract
The Conceptual Structures community has recently shown increased interest in methods and formalisms for the use of constraints in Conceptual Graphs (CGs), especially the definition of unification over constraints. None of the recent proposed constraint methods, however, are able to use simple unification methods, and still guarantee that a graph which is structurally valid under the canonical formation rules is also semantically valid in the knowledge domain. Our approach defines a method (and concept type) for constraining real values in the referent of a concept. The significance of our work is that a simple unification operation, using join and type subsumption, is defined which can be used to validate the constraints over an entire unified graph. A useful side-effect is that this constraint method can also be used to define real numbers in a referent.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Cao, T.H., P.N. Creasy, and V. Wuwongse. “Fuzzy Unification and Resolution Proof Procedure for Fuzzy Conceptual Graph Programs,” in Proc. Fifth International Conference on Conceptual Structures, August, 1997. Seattle, Washington, USA: Springer-Verlag. Published as Lecture Notes in Artificial Intelligence #1257.
Chein, M. and M.-L. Mugnier, “Conceptual Graphs: Fundamental Notions,” Revue d’Intelligence Artificielle, 1992. 6(4): p. 365–406.
Dibie, J., O. Haemmerl, and S. Loiseau. “A Semantic Validation of Conceptual Graphs,” in Proc. Sixth International Conference on Conceptual Structures, August, 1998. Montpellier, France: Springer-Verlag. Published as Lecture Notes in Artificial Intelligence #1453.
Kocura, P. “Conceptual Graphs and Semantic Constraints,” in Proc. Fourth International Conference on Conceptual Structures, August, 1996. Sydney, NSW, Australia: University of NSW Press.
Mineau, G.W. and R. Missaoui. “The Representation of Semantic Constraints in Conceptual Graph Systems,” in Proc. Fifth International Conference on Conceptual Structures, August, 1997. Seattle, Washinton, USA: Springer-Verlag. Published as Lecture Notes in Artificial Intelligence #1257.
Mugnier, M.-L. and M. Chein, “Repr senter des Connaissances et Raisonner avec des Graphes,” Revue d’Intelligence Artificielle, 1996. 10(6): p. 7–56.
MŸller, T., Conceptual Graphs as Terms: Prospects for Resolution Theorem Proving, 1997, Masters Thesis, Department of Computer Science, Vrije Universiteit Amsterdam, Amsterdam, Netherlands.
Sowa, J.F., Conceptual Structures: Information Processing in Mind and Machine. 1984, Reading, Mass: Addison-Wesley.
Van Hentenryck, P., Constraint Satisfaction in Logic Programming. Logic Programming, ed. E. Shapiro. 1989, Cambridge, Massachusetts, USA: MIT Press.
Van Hentenryck, P., L. Michel, and Y. Deville, Numerica. 1997, Cambridge, Massachusetts, USA: MIT Press.
Wille, R. “Conceptual Graphs and Formal Concept Analysis,” in Proc. Fifth International Conference on Conceptual Structures, August, 1997. Seattle, Washington, USA: Springer-Verlag. Published as Lecture Notes in Artificial Intelligence #1257.
Willems, M. “Projection and Unification for Conceptual Graphs,” in Proc. Third International Conference on Conceptual Structures, August, 1995. Santa Cruz, California, USA: Springer-Verlag. Published as Lecture Notes in Artificial Intelligence #954.
Wuwongse, V. and T.H. Cao. “Towards Fuzzy Conceptual Graph Programs,” in Proc. Fourth International Conference on Conceptual Structures, August, 1996. Sydney, Australia: Springer-Verlag. Published as Lecture Notes in Artificial Intelligence #1115.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Corbett, D., Woodbury, R. (1999). Unification over Constraints in 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_30
Download citation
DOI: https://doi.org/10.1007/3-540-48659-3_30
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66223-5
Online ISBN: 978-3-540-48659-6
eBook Packages: Springer Book Archive