Declarative Semantics for Active Rules

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In this paper we analyze declarative deterministic and non-deterministic semantics for active rules. In particular we consider several (partial) stable model semantics, previously defined for deductive rules, such as well-founded, max deterministic, unique total stable model, total stable model, and maximal stable model semantics. The semantics of an active program AP is given by first rewriting it into a deductive program P, then computing a model M defining the declarative semantics of P and, finally, applying `consistent' updates contained in M to the source database. The framework we propose permits a natural integration of deductive and active rules and can also be applied to queries with function symbols or to queries over infinite databases.