Dealing with context dependent knowledge has led to different formalizations of the notion of context. Among them is the Contextualized Knowledge Repository (CKR) framework. The CKR framework caters for reasoning with defeasible axioms and exceptions in contexts, which was extended to knowledge inheritance across contexts in a coverage (specificity) hierarchy. However, the approach supports only this single type of contextual relation and the reasoning procedures work only for restricted hierarchies.

In this project, we overcome these limitations and present a generalization of CKR hierarchies to multiple contextual relations, along with their interpretation of defeasible axioms and preference. We use ASP with algebraic measures. Notably, we show that for a relevant fragment of CKR hierarchies with multiple contextual relations, query answering can be realized with the popular asprin framework.