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

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 and preference. To support reasoning, we use ASP with algebraic measures, which is a recent extension of ASP with weighted formulas over semirings that allows one to associate quantities with interpretations depending on the truth values of propositional atoms. 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. The algebraic measures approach is more powerful and enables e.g. reasoning with epistemic queries over CKRs, which opens interesting perspectives for the use of quantitative ASP extensions in other applications.