The purpose of this paper is to explore the notion of consequence in Approximate Reasoning. While logical consequence has an standard (semantic and syntactic) definition in Exact Logic, several different definitions of that concept can be considered in the Approximate Reasoning framework. In this paper some definitions are compared with consequences derived from inference methods used in Artificial Intelligence. We will show that some inference methods are not covered by that definitions. Finally a more general concept of Approximate Consequence is introduced covering a wide variety of such inference methods.