Justifiable Exceptions in General Contextual Hierarchies

The problem of representing and reasoning with context dependent knowledge has recently gained interest in the area of description logics: among the several proposals, we consider the Contextualized Knowledge Repository (CKR) framework. In CKR applications it is often useful to reason over a hierarchical organization of contexts: for this reason, in our recent work we extended the CKR model to allow for the representation of exception handling in the inheritance of knowledge across contexts. However, to simplify the definition of reasoning procedures, we limited our approach to a particular kind of context organization, i.e. ranked hierarchies. In this paper, we further develop the proposal to extend the reasoning on exception handling for CKRs with general contextual hierarchies. We adapt the semantics (on a core version of CKR) to cope with contextual defeasible axioms in general hierarchies; on the base of this, we define an ASP based reasoning procedure that is complete w.r.t. instance checking under the proposed semantics for general contextual hierarchies.