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In Dung\u2019s abstract argumentation frameworks (AAFs), arguments interact negatively via an attack relation. Since then, a plethora of extensions have been proposed with the aim of expressing other common argument relationships. Two such proposals are bipolar argumentation frameworks (BAFs), in which both attack (negative) and support (positive) relations coexist; and frameworks with sets of attacking arguments (SETAFs), where attacks can be collective, originating from a set of arguments. In this paper, we show equivalences between a specific notion of support (\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\" overflow=\"scroll\">\n                        <mml:mi>\u03b2<\/mml:mi>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    -semantics) and of joint attacks in argumentation, by providing direct translations from BAFs and SETAFs (and vice versa) in a one-to-one correspondence between (BAF)\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\" overflow=\"scroll\">\n                        <mml:mi>\u03b2<\/mml:mi>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    -complete and (SETAF) complete labellings,\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\" overflow=\"scroll\">\n                        <mml:mi>\u03b2<\/mml:mi>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    -grounded and grounded labellings,\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\" overflow=\"scroll\">\n                        <mml:mi>\u03b2<\/mml:mi>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    -preferred and preferred labellings,\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\" overflow=\"scroll\">\n                        <mml:mi>\u03b2<\/mml:mi>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    -stable and stable labellings, and\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\" overflow=\"scroll\">\n                        <mml:mi>\u03b2<\/mml:mi>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    -semi-stable and semi-stable labellings. Besides semantic equivalences, we show structural (or syntactic) equivalences between BAFs and SETAFs by finding subsets of them for which the proposed translations are each other\u2019s inverse up to isomorphism.\n                  <\/jats:p>","DOI":"10.1177\/19462174261442070","type":"journal-article","created":{"date-parts":[[2026,4,19]],"date-time":"2026-04-19T22:50:12Z","timestamp":1776639012000},"page":"183-204","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["On the equivalence between bipolar argumentation frameworks and frameworks with sets of attacking arguments (SETAFs)"],"prefix":"10.1177","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9502-3413","authenticated-orcid":false,"given":"Renan","family":"Cordeiro","sequence":"first","affiliation":[{"name":"Department of Computer Science, Federal University of Cear\u00e1, Fortaleza, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4297-2970","authenticated-orcid":false,"given":"Jo\u00e3o","family":"Alc\u00e2ntara","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Federal University of Cear\u00e1, Fortaleza, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2026,4,19]]},"reference":[{"key":"e_1_3_3_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/0004-3702(94)00041-X"},{"key":"e_1_3_3_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11225-009-9218-x"},{"key":"e_1_3_3_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0004-3702(97)00015-5"},{"key":"e_1_3_3_5_2","unstructured":"Brewka G Woltran S. 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