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Reasoning on Multirelational Contextual Hierarchies via Answer Set Programming with Algebraic Measures

Published online by Cambridge University Press:  05 November 2021

LORIS BOZZATO Open the ORCID record for LORIS BOZZATO [Opens in a new window] ,
THOMAS EITER Open the ORCID record for THOMAS EITER [Opens in a new window]  and
RAFAEL KIESEL Open the ORCID record for RAFAEL KIESEL [Opens in a new window]
LORIS BOZZATO
Affiliation:
Fondazione Bruno Kessler, Via Sommarive 18, 38123 Trento, Italy (e-mail: bozzato@fbk.eu)
THOMAS EITER
Affiliation:
Technische Universit¨at Wien, Favoritenstraße 9-11, A-1040 Vienna, Austria (e-mails: thomas.eiter@tuwien.ac.at, rafael.kiesel@tuwien.ac.at)
RAFAEL KIESEL
Affiliation:
Technische Universit¨at Wien, Favoritenstraße 9-11, A-1040 Vienna, Austria (e-mails: thomas.eiter@tuwien.ac.at, rafael.kiesel@tuwien.ac.at)
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Abstract

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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 nontrivial 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, for example, reasoning with epistemic queries over CKRs, which opens interesting perspectives for the use of quantitative ASP extensions in other applications.

Keywords

defeasible knowledgedescription logicsASPalgebraic measuresjustifiable exceptions
Type
Original Article
Information
Theory and Practice of Logic Programming , Volume 21 , Issue 5: 37th International Conference on Logic Programming Special Issue I , September 2021 , pp. 593 - 609
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0), which permits unrestricted re- use, distribution and reproduction, provided the original article is properly cited.
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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