A type-theoretical approach for ontologies: The case of roles

International audienceIn the domain of ontology design as well as in Knowledge Representation, modeling universals is a challenging problem. Most approaches that have addressed this problem rely on Description Logics (DLs) but many difficulties remain, due to under-constrained representation which reduces the inferences that can be drawn and further causes problems in expressiveness. In mathematical logic and program checking, type theories have proved to be appealing but, so far they have not been applied in the formalization of ontologies. To bridge this gap, we present in this paper a theory for representing ontologies in a dependently-typed framework which relies on strong formal foundations including both a constructive logic and a functional type system. The language of this theory defines in a precise way what ontological primitives such as classes, relations, properties, etc., and thereof roles, are. The first part of the paper details how these primitives are defined and used within the theory. In a second part, we focus on the formalization of the role primitive. A review of significant role properties leads to the specification of a role profile and most of the remaining work details through numerous examples, how the proposed theory is able to fully satisfy this profile. It is demonstrated that dependent types can model several non-trivial aspects of roles including a formal solution for generalization hierarchies, identity criteria for roles and other contributions. A discussion is given on how the theory is able to cope with many of the constraints inherent in a good role representation

Relationships meet their roles in object oriented programming

Abstract. In this paper we study how roles can be added to patterns modelling relationships in Object Oriented programming. Relationships can be introduced in programming languages either by reducing them to attributes of the objects which participate in the relationship, or by modelling the relationship itself as a class whose instances have the participants of the relationships among their attributes. However, even if roles have been recognized as an essential component of relationships, also in modelling languages like UML, they have not been introduced in Object Oriented programming when it is necessary to model relationships. Introducing roles allows to add attributes and behaviors to the participants in the relationship, rather than to the relationship itself, and to distinguish the natural types of the participants in the relationships from the roles the participants acquire in the relationships. We show how the role model of the language powerJava can be used to endow the relationship as attribute pattern with roles.