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In this paper we investigate some issues arising from the introduction of multiple temporal granularities in an objectoriented data model. Although issues concerning temporal granularities have been investigated in the context of temporal relational database systems, no comparable amount of work has been done in the context of object-oriented models. Moreover, the main drawback of the existing proposals is the lack of a formal basis -which we believe is essential to manage the inherent complexity of the object-oriented data model. In this paper, we provide a complete temporal object-oriented type system supporting multiple temporal granularities and we formally define the set of legal values for our type system. We then address issues related to inheritance, type refinement and substitutability.

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An active database is a database in which some operations are automatically executed when speci ed events happen and particular conditions are met. Several systems supporting active rules in an object-oriented data model have been proposed. However, several issues related to the integration of triggers with object-oriented modeling concepts have not been satisfactorily addressed. In this paper, we discuss issues related to trigger inheritance and re nement in the context of the Chimera active object-oriented data model. In particular, we introduce a semantics for an active object language that takes into account trigger inheritance and supports trigger overriding. Moreover, we state conditions on trigger overriding ensuring that trigger semantics is preserved in subclasses. Keywords| Triggers, object-oriented data models, inheritance and re nement.