{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T03:44:53Z","timestamp":1777434293867,"version":"3.51.4"},"reference-count":13,"publisher":"SAGE Publications","issue":"2","license":[{"start":{"date-parts":[[2024,3,22]],"date-time":"2024-03-22T00:00:00Z","timestamp":1711065600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"},{"start":{"date-parts":[[2024,3,22]],"date-time":"2024-03-22T00:00:00Z","timestamp":1711065600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Argument &amp; Computation"],"published-print":{"date-parts":[[2025,6]]},"abstract":"<jats:p>Much like admissibility is the key concept underlying preferred semantics, strong admissibility is the key concept underlying grounded semantics, as membership of a strongly admissible set is sufficient to show membership of the grounded extension. As such, strongly admissible sets and labellings can be used as an explanation of membership of the grounded extension, as is for instance done in some of the proof procedures for grounded semantics. In the current paper, we present two polynomial algorithms for constructing relatively small strongly admissible labellings, with associated min\u2013max numberings, for a particular argument. These labellings can be used as relatively small explanations for the argument\u2019s membership of the grounded extension. Although our algorithms are not guaranteed to yield an absolute minimal strongly admissible labelling for the argument (as doing so would have implied an exponential complexity), our best performing algorithm yields results that are only marginally larger. Moreover, the runtime of this algorithm is an order of magnitude smaller than that of the existing approach for computing an absolute minimal strongly admissible labelling for a particular argument. As such, we believe that our algorithms can be of practical value in situations where the aim is to construct a minimal or near-minimal strongly admissible labelling in a time-efficient way.<\/jats:p>","DOI":"10.3233\/aac-230012","type":"journal-article","created":{"date-parts":[[2024,3,22]],"date-time":"2024-03-22T11:55:20Z","timestamp":1711108520000},"page":"212-236","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":2,"title":["Tractable algorithms for strong admissibility"],"prefix":"10.1177","volume":"16","author":[{"given":"Martin","family":"Caminada","sequence":"first","affiliation":[{"name":"Cardiff University","place":["United Kingdom"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sri","family":"Harikrishnan","sequence":"additional","affiliation":[{"name":"Vienna University of Economics and Business","place":["Austria"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2024,3,22]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.artint.2007.04.004"},{"key":"e_1_3_2_3_2","first-page":"111","author":"Caminada M.W.A.","year":"2006","unstructured":"Caminada M.W.A., On the issue of reinstatement in argumentation, in: Logics in Artificial Intelligence; 10th European Conference, JELIA 2006, Fischer M., van der Hoek W., Konev B., Lisitsa A., eds, Springer, 2006, pp.\u00a0111\u2013123, LNAI 4160.","journal-title":"Logics in Artificial Intelligence; 10th European Conference, JELIA 2006"},{"key":"e_1_3_2_4_2","first-page":"197","author":"Caminada M.W.A.","year":"2014","unstructured":"Caminada M.W.A., Strong admissibility revisited, in: Computational Models of Argument, Parsons S., Oren N., Reed C., Cerutti F., eds, Proceedings of COMMA 2014, IOS Press, 2014, pp.\u00a0197\u2013208.","journal-title":"Computational Models of Argument"},{"key":"e_1_3_2_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-28460-6_4"},{"key":"e_1_3_2_6_2","volume":"1","author":"Caminada M.W.A.","year":"2018","unstructured":"Caminada M.W.A., Baroni P., Giacomin M., Abstract argumentation frameworks and their semantics, in: Handbook of Formal Argumentation, Vol.\u00a01, College Publications, 2018.","journal-title":"Handbook of Formal Argumentation"},{"key":"e_1_3_2_7_2","doi-asserted-by":"publisher","DOI":"10.3233\/AAC-190463"},{"key":"e_1_3_2_8_2","first-page":"135","author":"Caminada M.W.A.","year":"2020","unstructured":"Caminada M.W.A., Dunne P.E., Minimal strong admissibility: A complexity analysis, in: Proceedings of COMMA 2020, Prakken H., Bistarelli S., Santini F., Taticchi C., eds, IOS Press, 2020, pp.\u00a0135\u2013146.","journal-title":"Proceedings of COMMA 2020"},{"key":"e_1_3_2_9_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11225-009-9218-x"},{"key":"e_1_3_2_10_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10458-009-9116-7"},{"key":"e_1_3_2_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/0004-3702(94)00041-X"},{"key":"e_1_3_2_12_2","first-page":"179","author":"Dvo\u0159\u00e1k W.","year":"2020","unstructured":"Dvo\u0159\u00e1k W., Wallner J., Computing strongly admissible sets, in: Proceedings of COMMA 2020, Prakken H., Bistarelli S., Santini F., Taticchi C., eds, IOS Press, 2020, pp.\u00a0179\u2013190.","journal-title":"Proceedings of COMMA 2020"},{"key":"e_1_3_2_13_2","first-page":"105","author":"Modgil S.","year":"2009","unstructured":"Modgil S., Caminada M.W.A., Proof theories and algorithms for abstract argumentation frameworks, in: Argumentation in Artificial Intelligence, Rahwan I., Simari G.R., eds, Springer, 2009, pp.\u00a0105\u2013129. doi:https:\/\/doi.org\/10.1007\/978-0-387-98197-0_6.","journal-title":"Argumentation in Artificial Intelligence"},{"key":"e_1_3_2_14_2","doi-asserted-by":"publisher","DOI":"10.1093\/comjnl\/bxz138"}],"container-title":["Argument &amp; 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