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Dealing with context dependent knowledge has led to different formalizationsof the notion of context. Among them is the Contextualized Knowledge Repository(CKR) framework, which is rooted in description logics but links on thereasoning side strongly to logic programs and Answer Set Programming (ASP) inparticular. The CKR framework caters for reasoning with defeasible axioms andexceptions in contexts, which was extended to knowledge inheritance acrosscontexts in a coverage (specificity) hierarchy. However, the approach supportsonly this single type of contextual relation and the reasoning procedures workonly for restricted hierarchies, due to non-trivial issues with modelpreference under exceptions. In this paper, we overcome these limitations andpresent a generalization of CKR hierarchies to multiple contextual relations,along with their interpretation of defeasible axioms and preference. To supportreasoning, we use ASP with algebraic measures, which is a recent extension ofASP with weighted formulas over semirings that allows one to associatequantities with interpretations depending on the truth values of propositionalatoms. Notably, we show that for a relevant fragment of CKR hierarchies withmultiple contextual relations, query answering can be realized with the popularasprin framework. The algebraic measures approach is more powerful and enablese.g. reasoning with epistemic queries over CKRs, which opens interestingperspectives for the use of quantitative ASP extensions in other applications.

Reasoning on Multi-Relational Contextual Hierarchies via Answer Set Programming with Algebraic Measures