This paper investigates a new approach for computing ap- proximate answers of ontological queries based on a notion of an edit distance of a given individual w.r.t. a given query. Such a distance is computed by counting the number of elementary operations needed to be applied to an ABox in order to make a given individual a correct an- swer to a given query. The considered elementary operations are adding to or removing from an ABox, assertions of the form of an atomic con- cept (or its negation) and/or atomic roles. We describe some preliminary results regarding the problem of computing such approximate answers in the context of the Open World Assumption (OWA) and the Generalized Closed World Assumption (GCWA) approaches.