  As ontologies and description logics (DLs) reach out to a broader audience,
several reasoning services are developed in this context. Belief revision is
one of them, of prime importance when knowledge is prone to change and
inconsistency. In this paper we address both the generalization of the
well-known AGM postulates, and the definition of concrete and well-founded
revision operators in different DL families. We introduce a model-theoretic
version of the AGM postulates with a general definition of inconsistency, hence
enlarging their scope to a wide family of non-classical logics, in particular
negation-free DL families. We propose a general framework for defining revision
operators based on the notion of relaxation, introduced recently for defining
dissimilarity measures between DL concepts. A revision operator in this
framework amounts to relax the set of models of the old belief until it reaches
the sets of models of the new piece of knowledge. We demonstrate that such a
relaxation-based revision operator defines a faithful assignment and satisfies
the generalized AGM postulates. Another important contribution concerns the
definition of several concrete relaxation operators suited to the syntax of
some DLs (ALC and its fragments EL and ELU).
