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

arXiv: https://arxiv.org/abs/2108.03100 · HTML: https://mlsanity.com/paper/2108.03100/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 30 references that are in the map.
- First posted on arXiv 6 Aug 2021.

## Builds on (most cited first, 2 of 2)

- [An ASP approach for reasoning in a concept-aware multipreferential lightweight DL](https://mlsanity.com/paper/2006.04387/) (2020)
- [On the Non-Monotonic Description Logic ALC+T_mathsfmin](https://mlsanity.com/paper/1404.6566/) (2014)

## Built on by (most cited first, 4 of 4)

- [Complexity and scalability of defeasible reasoning in many-valued weighted knowledge bases with typicality](https://mlsanity.com/paper/2303.04534/) (2023)
- [A preferential interpretation of MultiLayer Perceptrons in a conditional logic with typicality](https://mlsanity.com/paper/2305.00304/) (2023)
- [Contextual Reasoning for Scene Generation (Technical Report)](https://mlsanity.com/paper/2305.02255/) (2023)
- [A framework for Conditional Reasoning in Answer Set Programming](https://mlsanity.com/paper/2506.03997/) (2025)

## Abstract (arXiv)

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.