There have been many recent research efforts on temporal databases for managing current and historical data and on active databases for monitoring real-world events as well as data conditions/constraints by rules and triggers. However, the specification and management of temporal rules in active object-oriented databases has not been investigated. This paper deals with the specification and management of temporal requirements and constraints of real-world applications. We present a temporal

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... ledge model in which temporal rules are defined as part of the semantic specifications of object instances and object classes. We also present a temporal specification language which is characterized by its validity time specification, its trigger specification that involves time and system-and user-defined operations, and the inclusion of temporal conditions and association patterns in temporal rules. Three general types of temporal rules are distinguished: state rules for specifying the legitimate or illegitimate states of a temporal knowledge base, operational rules for specifying the operations to be taken under various temporal conditions, and deductive rules for deducing objects' data values and object associations which are not explicitly stored. Activations of temporal rules are controlled by triggers which specify the various times and conditions for rule evaluation. Rules can be updated resulting in historical rules. Rules can be inherited in a superclass-subclass hierarchy or a lattice as the inheritance of attributes and operations in the object-oriented paradigm. Temporal rules are modeled as first class objects and thus can be managed uniformly as temporal data by a temporal knowledge base management system. The methods for updating, retrieving, triggering, and evaluating temporal rules are also presented.