In this paper, we address the problem of applying AGM-style belief revision to non-classical logics. We discuss the idea of minimal change in revision and show that for non-classical logics, some sort of minimality postulate has to be explicitly introduced. We also present two constructions for revision which satisfy the AGM postulates and prove the representation theorems including minimality postulates.

In many scenarios where the integration of information into a knowledge base (KB) leads to inconsistencies there is a need to change the KB minimally. In belief revision, relevance postulates meet the minimality requirement by restricting the elimination of KB elements to those that are relevant for the incoming information. This paper focuses on two minimality postulates in an ontology revision scenario in which conflicts are caused by ambiguous use of symbols: a relevance postulate and a generalized inclusion postulate which limits the creativity of the operators. Both postulates exploit the (satisfiably) equivalent representation of a first-order logic KB by its prime implicates, which, intuitively, represent the most atomic logical components of the KB. The paper shows that reinterpretation operators (which are ontology revision operators) fulfill both postulates.