{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T10:28:15Z","timestamp":1776680895573,"version":"3.51.2"},"reference-count":24,"publisher":"Cambridge University Press (CUP)","issue":"5-6","license":[{"start":{"date-parts":[[2019,9,20]],"date-time":"2019-09-20T00:00:00Z","timestamp":1568937600000},"content-version":"unspecified","delay-in-days":19,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Theory and Practice of Logic Programming"],"published-print":{"date-parts":[[2019,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Abstract Dialectical Frameworks (<jats:italic>ADF<\/jats:italic>s) are argumentation frameworks where each node is associated with an acceptance condition. This allows us to model different types of dependencies as supports and attacks. Previous studies provided a translation from Normal Logic Programs (<jats:italic>NLP<\/jats:italic>s) to<jats:italic>ADF<\/jats:italic>s and proved the stable models semantics for a normal logic program has an equivalent semantics to that of the corresponding<jats:italic>ADF<\/jats:italic>. However, these studies failed in identifying a semantics for<jats:italic>ADF<\/jats:italic>s equivalent to a three-valued semantics (as partial stable models and well-founded models) for<jats:italic>NLP<\/jats:italic>s. In this work, we focus on a fragment of<jats:italic>ADF<\/jats:italic>s, called Attacking Dialectical Frameworks (<jats:italic>ADF<\/jats:italic><jats:sup>+<\/jats:sup>s), and provide a translation from<jats:italic>NLP<\/jats:italic>s to<jats:italic>ADF<\/jats:italic><jats:sup>+<\/jats:sup>s robust enough to guarantee the equivalence between partial stable models, well-founded models, regular models, stable models semantics for<jats:italic>NLP<\/jats:italic>s and respectively complete models, grounded models, preferred models, stable models for<jats:italic>ADF<\/jats:italic>s. In addition, we define a new semantics for<jats:italic>ADF<\/jats:italic><jats:sup><jats:italic>+<\/jats:italic><\/jats:sup>s, called<jats:italic>L<\/jats:italic>-stable, and show it is equivalent to the<jats:italic>L<\/jats:italic>-stable semantics for<jats:italic>NLP<\/jats:italic>s.<\/jats:p>","DOI":"10.1017\/s1471068419000280","type":"journal-article","created":{"date-parts":[[2019,9,20]],"date-time":"2019-09-20T13:06:21Z","timestamp":1568984781000},"page":"941-956","source":"Crossref","is-referenced-by-count":7,"title":["On the Equivalence Between Abstract Dialectical Frameworks and Logic Programs"],"prefix":"10.1017","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4297-2970","authenticated-orcid":false,"given":"JO\u00c3O","family":"ALC\u00c2NTARA","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"SAMY","family":"S\u00c1","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"JUAN","family":"ACOSTA-GUADARRAMA","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2019,9,20]]},"reference":[{"key":"S1471068419000280_ref22","unstructured":"Strass, H. 2013. 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