Summary: We introduce the notion of \(X\)-stable models parametrized by a given logic \(X\). This notion is based on a construction that we call weak completion: a set of atoms \(M\) is an \(X\)-stable model of a theory \(T\) if \(M\) is a model of \(T\), in the sense of classical logic, and the weak completion of \(T\) (namely \(T\cup\neg \widetilde M)\) can prove, in the sense given by the logic \(X\), every atom in the set \(M\). We prove that, for normal logic programs, the result obtained by these weak completions is invariant with respect to a large family of logics. Two kinds of logics are mainly considered: paraconsistent logics and normal modal logics. For modal logics we use a translation proposed by Gelfond that identifies \(\neg\square a\) with \(\neg a\). As a consequence we prove that several semantics (recently introduced) for nonmonotonic reasoning (NMR) are equivalent for normal programs. In addition, we show that such semantics can be characterized by a fixed-point operator. Also, as a side effect, we provide new results for the stable model semantics.