An abstract way to define rewriting logic

International audienceSince rewriting logic has been introduced, it has shown its adequateness both as a semantic and a logical framework. But the numerous applications of the rewriting logic in the above two areas has shown the importance of increasing its expressive power. Therefore, in order to facilitate this work, we will study in this paper how to generalize the transformation that from the equational logic has resulted in the rewriting logic. To achieve this purpose, we will show that there exists a valid and useful notion of rewriting logic associated to any rewriting theory fitting an abstract framework developed by two of the authors in previous papers