The Herbrand model H of a de nite logic program P is an initial model among the class of all the models of P, interpreting P as an initial theory. Such a theory proves (computes) only positive literals (atoms) in P, so it does not deal with negation. In this paper, we introduce isoinitial models of logic programs. We show that isoinitial semantics deals with negation, and works in a uniform way for de nite and normal logic programs. Moreover, the lack of an isoinitial model signals the absence of information. Thus it also provides a unifying semantics for closed and open logic programs.