Reasoning on Multi-Relational Contextual Hierarchies via Answer Set Programming with Algebraic Measures
Loris Bozzato, Thomas Eiter, Rafael Kiesel

TL;DR
This paper extends the CKR framework to handle multiple contextual relations and defeasible reasoning using ASP with algebraic measures, enabling more expressive and quantitative reasoning over context hierarchies.
Contribution
It generalizes CKR hierarchies to multiple relations and integrates algebraic measures into ASP for enhanced reasoning capabilities.
Findings
Generalized CKR hierarchies to multiple relations
Implemented reasoning with algebraic measures in ASP
Enabled epistemic query answering over CKRs
Abstract
Dealing with context dependent knowledge has led to different formalizations of the notion of context. Among them is the Contextualized Knowledge Repository (CKR) framework, which is rooted in description logics but links on the reasoning side strongly to logic programs and Answer Set Programming (ASP) in particular. 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, due to non-trivial issues with model preference under exceptions. In this paper, we overcome these limitations and present a generalization of CKR hierarchies to multiple contextual relations, along with their interpretation of defeasible axioms…
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