In the AGM paradigm for belief revision, epistemic states are represented by logically closed sets of sentences, the so-called belief sets.An alternative approach uses belief bases, arbitrary sets of sentences.Both approaches have their problems when it comes to contraction operations.Belief bases are more expressive, but, at the same time, they present a serious syntax dependence.Between those two extremes lie a whole gamut of operations called pseudo-contractions, some of which may be interesting alternatives to the classical ones, providing a good balance between syntax dependence and expressivity.In this paper we explore some very natural and general constructions for pseudocontractions, showing some of their properties and giving their axiomatic characterizations.We also illustrate possible practical scenarios where they can be employed.

Belief Revision deals with the problem of adding new information to a knowledge base in a consistent way. Ontology Debugging, on the other hand, aims to find the axioms in a terminological knowledge base which caused the base to become inconsistent. In this article, we propose a belief revision approach in order to find and repair inconsistencies in ontologies represented in some description logic (DL). As the usual belief revision operators cannot be directly applied to DLs, we propose new operators that can be used with more general logics and show that, in particular, they can be applied to the logics underlying OWL-DL and Lite.