Reasoning with Justifiable Exceptions in Contextual Hierarchies

The problem of reasoning with context dependent knowledge has recently gained interest in the area of description logic-based knowledge bases (KBs). Among the several proposals, we consider the Contextualized Knowledge Repository (CKR) framework. The CKR model has been recently extended with the capability of reasoning with global (context independent) defeasible axioms that can be overridden by local (context specific) knowledge. In CKR applications it is often useful to reason over a hierarchical organization of contexts. We highlight here our recent efforts on extending the CKR framework to allow for the representation of exception handling in the inheritance of knowledge across local contexts. We first concentrated on a limitation to a particular kind of context organization, i.e., ranked hierarchies, which allows us to simplify the definition of reasoning procedures. We then further generalized the proposal to extend the reasoning on exception handling over general contextual hierarchies. In this paper we summarize the basic definitions for simple CKRs with Justifiable Exceptions, the emerging computational properties, and the ASP-based reasoning procedures that we developed. Moreover, we highlight the open challenges in generalizing the approach and our future directions.