  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.
