Abstract
This paper proposes a method, called iO2, for building the inheritance graph of an O2 database schema. The iO2 method is based on the Galois lattice data structure. It encompasses three steps: a (first) construction step, a (second) optimization step, and a (final) generation step. This paper focuses on the two first steps.
The construction step builds the Galois graph of the finite binary relation associating properties to entity and relationship types. A new algorithm is proposed for this first step. The optimization step builds the Galois inheritance graph from the Galois graph. A new algorithm is proposed for this second step in order to eliminate the redundancies. The generation step yields the O2 inheritance graph from the Galois inheritance graph. The transformation principles underlying this third step are given. The detailed generation algorithm is presented in [Yah96a].
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References
M. Adiba, and C. Collet,“Objets et bases de données: le SGBD O2”. Ed. Hermes, 1993.
E. Amiel, M. J. Bellosta, E. Dujardin, and E. Simon,“Supporting exceptions to behavioral schema consistency to ease schema evolution in OODMS”. In Proceedings of the 20th International Conference on Very Large Databases-VLDB94., Chile 1994, pp. 108–119.
P. Baptiste, and J. Favrel, “Résolution de problèmes d'ordonnancement par les treillis de Galois et les graphes d'intervalle”. RAIRO-Automatique/Systems Analysis and Control, 1984, Vol. 18, Nℴ 4, pp. 405–416.
S. Bergamashi, and C. Sartori, “On taxonomic reasoning in conceptual design”. ACM Transactions on Database Systems, Vol. 17, Nℴ 3, September 1992, pp. 385–422.
G. Booch,“Object-oriented design with applications”. Benjamin/ Cumming Company, 1991.
J. P. Bordat, “Calcul pratique du treillis de Galois d'une correspondance”. Mathématiques et Sciences Humaines, Nℴ 96, 1986, pp. 31–47.
J.P. Bordat,“L'algorithmique combinatoire d'ordres finis”. Phd Thesis, Université de Montpellier II, 1992.
R. J. Brachman,“What ISA is and isn't”. Analysis of Taxonomic Links in semantic Network, Computer Nℴ10, 1983.
L. Cardelli,“A semantics of multiple inheritance”. Readings in Object-Oriented Database Systems, S. B. Zdonik and D. Maier (Eds.), 1990. pp. 51–67.
C. Carpineto, and G. Romano,“GALOIS: An order-theoretic approach to conceptual clustering”. Proceedings of the Machine Learning Conference, 1993, pp. 33–40.
P. Coad, and E. Yourdon,“ Object-oriented analysis”. Yourdon Press Computing Series, 1990.
W. R. Cook, and J. Palsberg,“A denotational semantics of inheritance and its correctness”. In proceedings of the International Conference On Object-Oriented Programming Languages and Applications-OOPSLA89, 1989, pp. 433–443.
W. R. Cook,“Interfaces and specifications for the smaltalk-80 collection class”. In proceedings of the International Conference On Object-Oriented Programming Languages and Applications-OOPSLA92, 1992, pp. 1–15.
C. Delcourt, and R. Zicari, “The design of an integrity consistency checker (ICC) for an object oriented database system”. European Conference on Object Oriented Programming-ECOOP 91. LNCS Nℴ 512, Geneva, Switzerland, July 1991. pp. 97–117.
R. Ducournau, M. Habib, M. Huchard, and M. L. Mugnier,“Monotonic conflict resolution mechanisms for inheritance”. In proceedings of the International Conference On Object-Oriented Programming Languages and Applications-OOPSLA92, 1992, pp. 16–24.
A. Formica, and M. Missikoff, “Correctness of ISA hierarchies in object-oriented database schemas”. In proceedings of the 4th International Conference on Extending Database Technology-EDBT 94, LNCS Nℴ 779, Cambridge, United Kingdom, March 1994, pp. 231–244.
R. Godin, and H. Mili,“Building and maintaining analysis-level class hierarchies using Galois lattices”. In proceedings of the International Conference On Object-Oriented Programming Languages and Applications-OOPSLA 93, 1993, pp. 394–410.
R. Godin, G. Mineau, R. Missaoui, and H. Mili, “Conceptual clustering methods based on Galois lattices and applications”. French Review on Artificial intelligence, Vol. 9, Nℴ 2, 1995, pp. 105–137.
R. Godin, G. W. Mineau, and R. Missaoui,“Incremental structuring of knowledge bases”. In proceedings of the International KRUSE Symposium, Callifornia, 1995, pp. 179–193.
R. Godin, R. Missaoui, and H. Alaoui, “Incremental concept formation algorithms based on Galois (concept) lattices”. In Computational Intelligence, Vol. 11, Nℴ2, 1995, pp. 246–265.
A. Guénoche, “Construction du treillis de Galois d'une relation binaire”. Mathématiques et Sciences Humaines, Nℴ 109, 1990, pp. 41–53.
R. Johnson, and B. Foote,“Designing reusable classes”. Journal of Object-Oriented Programming, June/July, 1988, pp-22–35.
T. Korson, and J. D. McGregor,“Technical criteria for the specification and evaluation of object-oriented Libraries”. Software Engineering Journal, March 1992, pp. 85–94.
C. Lécluse, P. Richard, and F. Velez“ O2, an object-oriented data model”. In proceedings of the ACM SIGMOD International Conference On Management of Data. June 1988, pp. 424–433.
K.J. Lieberherr, P.Bergstein, and I.Silvalep,“From objects to classes: algorithms for optional object-oriented design”. Journal of Software Engineering. July 1991, pp. 205–228.
M. Missikoff, and M. Scholl, “An algorithm for insertion into a lattice: application to type classification”. Foundations of Data Organization and Algorithms, 3rd International Conference-FODO89, Paris, France, June 1989, LNCS Nℴ 367, pp. 64–82.
P. Poncelet, M. Teisseire, R. Cicchetti, and L. Lakhal,“Towards a formal approach for object-oriented database design”. In Proceedings of the 19th International Conference on Very Large Databases-VLDB 93, Dublin, Ireland. August 1993, pp. 278–289.
J. Rumbaugh, M. Blaha, W. Premerlani, F. Eddy, and W. Lorensen, “Object oriented modeling and design”. Prentice Hall, 1991.
R. Taouil, L. Lakhal, and J.P. Bordat, “Evolutive building of Galois lattices”. Technical Report of LIMOS, Clermont-Ferrand University, Avril 1996.
R. Wille,“Restructuring lattice theory: An Approach Based on Hierarchies of Concepts”. In Ordered Sets, I. Rival (Eds.), 1982, pp. 445–470.
R. Wille, “Concept lattices and conceptual knowledge systems”. Computers Math. Applications Vol. 23, No. 6–9, 1992, pp. 493–515.
A. Yahia,“Restructuring the Galois inheritance graph”. Technical Report of LIMOS, Clermont-Ferrand University, September 1995.
A. Yahia, L. lakhal, and R. Cicchetti, “Building inheritance graphs in object database design”. DEXA' 96 Conference, Zurich, 9th–13th September 1996.
A. Yahia, L. lakhal, R. Cicchetti, and J. P. Bordat,“Conceptual modelling and design of class hierarchies in object database design”. In revision stage for The Computer Journal, 1996.
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Yahia, A., Lakhal, L., Cicchetti, R., Bordat, J.P. (1996). IO2 an algorithmic method for building inheritance graphs in object database design. In: Thalheim, B. (eds) Conceptual Modeling — ER '96. ER 1996. Lecture Notes in Computer Science, vol 1157. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0019938
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DOI: https://doi.org/10.1007/BFb0019938
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