The IsaLog model and language are presented. The model has complex objects with classes, relations, and is a hierarchies. The language is strongly types and declarative. The main issue is the definition of the semantics of the language, given in three different ways that are shown to be equivalent: a model-theoretic semantics, a reduction to logic programming with function symbols, and a fixpoint semantics. Each of the semantics presents new aspects with respect to existing proposals because of the interaction of oid-invention with general is a hierarchies. The solutions are based on the explicit Skolem functors, which provide a powerful tool for manipulating object-identifiers