Logic in Databases 

Abstract: After briefly reviewing the basic notions and terminology of active rules and relating them to production rules and deductive rules, respectively, we survey a number of formal approaches to active rules. Subsequently, we present our own state-oriented logical approach to active rules which combines the declarative semantics of deductive rules with the possibility to define updates in the style of production rules and active rules. The resulting language Statelog is surprisingly simple, yet captures many features of active rules including composite event detection and different coupling modes. Thus, it can be used for the formal analysis of rule properties like termination and expressive power. Finally, we show how nested transactions can be modeled in Statelog, both from the operational and the model-theoretic perspective.

Abstract: In this paper we take a first step towards characterizing active databases. Declarative characterization of active databases allows additional flexibility in studying the effects of different priority criteria between fireable rules, different actions and event definitions, and also to make claims about effects of transaction and prove them without actually executing them. Our characterization is related but different from similar attempts by Zaniolo in terms of making a clear distinction between actual and hypothetical execution of actions and allowing non-determinism. We use the ‘choice’ construct [SZ90] to characterize the non-determinism that arises when several rules can fire at the same time and the preference between them is not specified. We show through examples how our language allows us to express features of different active database systems.

Abstract: We present a hierarchically structured transaction-oriented concept for a rule-based active database system. In Report No.59 and Report No.78, we have proposed Statelog as a unified framework for active and deductive rules. Following the need for better structuring capabilities, we introduce procedures as a means to group semantically related rules and to encapsulate their behavior. In addition to executing elementary updates, procedures can be called, thereby defining (sub)transactions which may perform complex computations. A Statelog procedure is a set of ECA-style Datalog rules together with an import/export interface. System-immanent frame and procedure rules ensure both propagation of facts and processing of results of committed subtransactions. Thus, Statelog programs specify a nested transaction model which allows a much more structured and natural modeling of complex transactions than previous approaches. Two equivalent semantics for a Statelog program P are given: (i) a logic programming style semantics by a compilation into a logic program, and (ii) a model-theoretic Kripke-style semantics. While (ii) serves as a conceptual model of active rule behavior and allows to reason about properties of the specified transactions, (i) -- together with the appropriate execution model -- yields an operational semantics and can be used as an implementation of P.