A formal method for inheritance graph hierarchy construction

In [M.M. Gammoudi et al., in: Proceedings Lecture Notes of the International Conference on Conceptual Modeling ER'97, Los Angeles, November 1997; M.M. Gammoudi et al., in: The 18th International Conference on Conceptual Modelling (ER'99), Paris, November 15-18, Lecture Notes, Springer, Berlin, 1999] we proposed a semi-automatic method for generating inheritance graph hierarchy for the purpose of assisting the designer during the definition of his conceptual schema. The motivation for this work was the very few approaches which attempt to provide methods and tools for designing inheritance graph in object databases [R. Wille, in: E. Diday (Ed.), Data Analysis, Learning Symbolic and Numeric Knowledge, Nova Science, New York, 1989], and object software [A.L. Winblad et al., Object-Oriented Software, Addison-Wesley, New York, 1990]. To address some limitations found in our work, we propose a new method whose principles are: (i) From a binary relation which represents the links between entities and their properties and methods, our proposed heuristic generates and organizes incrementally a set of optimal rectangles into a brut inheritance graph (BIG). (ii) BIG is refined and submitted to the designer. (iii) The designer can modify, add or remove classes, attributes or methods in the binary relation and activate step (i) until he obtains a proper class hierarchy or an optimal inheritance graph.