The hierarchical representation of binary relations: application to the design of class hierarchies
International Journal of Computing and Optimization
This work is about formalizing the hierarchical nature of binary relations. We introduce a new representation for binary relations called the inheritance graph of the binary relation and denoted by H(R). We also present the concept of Isa hierarchy for abstracting class hierarchies. It is both formal and general. Indeed, no assumption is made about the underlying data model. Every where a binary relation holds, its corresponding inheritance graph may have potential benefits. These may be
... These may be tremendous with regard to the wide range of applications and the correctness of the formal representation. Among the approaches for constructing class hierarchies, we can find conceptual clustering methods and taxonomic reasoning  , classification and learning methods . We can also find approaches which are devoted to specific computer domains such as database design   and software engineering  . Nevertheless what method is used or what application is considered, the general representation of a class hierarchy is that of a directed acyclic graph (DAG). This opens doors for formalization without being obliged to specify a particular data model.