In this paper, we present a type model for object-oriented databases. Most object-oriented databases only provide users with flat objects whose structure is a record of other objects. In order to have a powerful expression power, an object-oriented database should not only provide objects but also complex values recursively built using the set, tuple and disjunctive constructors. Our type model presents two notions: that of classes whose instances are objects with identity and that of types whose instances are complex values. The two notions are mixed in that an object is modeled as a pair containing an identifier and a value, and a value is a complex structure which contains objects and values. We define in this context the notions of subtyping and provide a set inclusion semantics for subtyping.

The Altair group is currently designing an object-oriented data base system called O 2 . This paper presents a formal description of the object-oriented data model of this system. It proposes a type system defined in the framework of a set-and-tuple data model. It models the well known inheritance mechanism and enforces strong typing.

We present a set-theoretic interpretation of the relational model which allows a semantic approach to query answering. We show that deduction of new tuples from those in the database is possible through set-containment and we give an algorithm for deductive query-answering.