{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T00:55:51Z","timestamp":1768438551286,"version":"3.49.0"},"reference-count":29,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[2021,11,5]],"date-time":"2021-11-05T00:00:00Z","timestamp":1636070400000},"content-version":"unspecified","delay-in-days":65,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["Theory and Practice of Logic Programming"],"published-print":{"date-parts":[[2021,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>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.<\/jats:p>","DOI":"10.1017\/s1471068421000284","type":"journal-article","created":{"date-parts":[[2021,11,5]],"date-time":"2021-11-05T14:49:45Z","timestamp":1636123785000},"page":"593-609","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":7,"title":["Reasoning on Multirelational Contextual Hierarchies via Answer Set Programming with Algebraic Measures"],"prefix":"10.1017","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1757-9859","authenticated-orcid":false,"given":"LORIS","family":"BOZZATO","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6003-6345","authenticated-orcid":false,"given":"THOMAS","family":"EITER","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8866-3452","authenticated-orcid":false,"given":"RAFAEL","family":"KIESEL","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2021,11,5]]},"reference":[{"key":"S1471068421000284_ref14","doi-asserted-by":"publisher","DOI":"10.1016\/j.artint.2008.04.002"},{"key":"S1471068421000284_ref9","article-title":"Principles of KLM-style defeasible description logics","volume":"1","author":"Britz","year":"2021","journal-title":"ACM Transactions on Computational Logic 22"},{"key":"S1471068421000284_ref5","doi-asserted-by":"crossref","unstructured":"Bozzato, L. , Eiter, T. and Serafini, L. 2019. Justifiable exceptions in general contextual hierarchies. In Proc. Context 2019, G. Bella and P. Bouquet, Eds. LNCS, vol. 11939. Springer, 26\u201339.","DOI":"10.1007\/978-3-030-34974-5_3"},{"key":"S1471068421000284_ref10","unstructured":"Buccafurri, F. , Faber, W. and Leone, N. 1999. Disjunctive logic programs with inheritance. In Proceedings of ICLP 1999, D. D. Schreye, Ed. MIT Press, 79\u201393."},{"key":"S1471068421000284_ref15","first-page":"729","volume-title":"Proceedings of ECAI 2020","author":"Eiter","year":"2020"},{"key":"S1471068421000284_ref21","first-page":"31","volume-title":"Proceedings of PODS 2007","author":"Green","year":"2007"},{"key":"S1471068421000284_ref1","unstructured":"Baader, F. , Calvanese, D. , McGuinness, D. , Nardi, D. and Patel-Schneider, P. , Eds. 2003. The Description Logic Handbook. 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Reasoning with justifiable exceptions in contextual hierarchies. In Proceedings of KR 2018. AAAI Press, 329\u2013338."},{"key":"S1471068421000284_ref4","doi-asserted-by":"publisher","DOI":"10.1016\/j.artint.2017.12.005"},{"key":"S1471068421000284_ref28","doi-asserted-by":"publisher","DOI":"10.1016\/j.websem.2011.12.003"},{"key":"S1471068421000284_ref27","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijar.2018.08.005"},{"key":"S1471068421000284_ref25","doi-asserted-by":"crossref","unstructured":"Kr\u00f6tzsch, M. 2010. Efficient inferencing for OWL EL. In Proceedings of JELIA 2010. Springer, 234\u2013246.","DOI":"10.1007\/978-3-642-15675-5_21"},{"key":"S1471068421000284_ref3","first-page":"1","article-title":"A new semantics for overriding in description logics","author":"Bonatti","year":"2015","journal-title":"Artificial Intelligence 222"},{"key":"S1471068421000284_ref24","unstructured":"Klarman, S. 2013. Reasoning with contexts in description logics. 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Published by Cambridge University Press","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"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.","name":"license","label":"License","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}