This work sets out the main ideas concerning a semantics of possible worlds for epistemic logics which do not have the problem of logical omniscience and which can be used to model reasoning with limited resources. Within this semantic system, possible worlds are defined through a constructive process which is used to define a relation of accessibility between worlds, which is generally treated as a primitive notion. Furthermore, the concepts of logical omniscience and ideal reasoning, usually considered as synonymous in the literature, are formally described. This formal description can be used to show that the alternatives which have been presented to avoid logical omniscience have not satisfactorily resolved the fundamental problem. In addition, the concept of possible worlds is formulated in purely syntactic terms in order to present the main ideas underlying a model of local reasoning which can be applied in a wide range of disciplines.