Specialization by Restriction and Schema Derivations

Specialization and inheritance are well-known concepts in the area of object-oriented modelling and knowledge representation. However, certain aspects of these concepts lack formal foundations. In particular, when properties of diierent classes are semantically related, several different semantics are possible for the inherited properties, and a choice is necessary. Conventional systems impose an a priori solution that supports only one of the possible semantics of inheritance. In this paper, we present constructs that allow to diierentiate between the possible semantics of inheritance, in a formal and sound way. Our approach is based on a structured view of the real world and a model for its representation. By necessity, the model only partly represents the real world. Thus, reasoning in the model is done with reference to the real world. We introduce restriction isa, a form of specialization that represents property restriction, and demonstrate that it can be a useful conceptual modelling mechanism. We employ restriction isa to formally deene property inheritance. Reasoning in our model is done through a number of inference rules that reeect real world constraints. These rules allow for sound derivations both at instance and schema level. At the schema level, in particular, these rules allow to relate inherited properties to other properties through restriction-isa and isa relations. Such relations not only give useful information about the inherited properties but also reene the value domains of these properties.