The aim of our work is the definition of compositional semantics for modular units over the class of normal logic programs. In this sense, we propose a declarative semantics for normal logic programs in terms of model classes that is monotonic in the sense that Mod(PUP') is included in Mod(P), for any programs P and P', and we show that in the model class associated to every program there is a least model that can be seen as the semantics of the program, which may be built upwards as the least fix point of a continuous immediate consequence operator. In addition, it is proved that this least model is "typical" for the class of models of the Clark-Kunen's completion of the program. This means that our semantics is equivalent to Clark-Kunen's completion. On the other hand, following the approach defined in a previous paper, it is shown that our semantics constitutes a "specification frame" equipped with the adequate categorical constructions needed to define compositional and fully abstract (categorical) semantics for a number of program units. In particular, we provide acategorical semantics of arbitrary normal logic program fragments which is compositionaland fully abstract with respect to the (standard) union.