The development of formal systems for reasoning about knowledge is one of the main research issues in Artificial Intelligence. A reoccuring problem in most of the systems is the one of logical omniscience or consequential closure which expresses the notion that when a reasoning agent knows anything he knows all its logical cosequences. This result is neither intuitively admissable nor computationally feasible. The paper explores the possibilities of restricting the omniscience in an intensional context.