Possibilistic Logic Underlies Abstract Dialectical Frameworks

Jesse Heyninck, Gabriele Kern-Isberner, Tjitze Rienstra, Kenneth Skiba, Matthias Thimm

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Abstract dialectical frameworks (in short, ADFs) are one of the most general and unifying approaches to formal argumentation. As the semantics of ADFs are based on three-valued interpretations, we ask which monotonic three-valued logic allows to capture the main semantic concepts underlying ADFs. We show that possibilistic logic is the unique logic that can faithfully encode all other semantical concepts for ADFs. Based on this result, we also characterise strong equivalence and introduce possibilistic ADFs.

Original languageEnglish
Title of host publicationProceedings of the Thirty-First International Joint Conference on Artificial Intelligence (IJCAI-22)
PublisherInternational Joint Conferences on Artificial Intelligence
ISBN (Electronic)978-1-956792-00-3
Publication statusPublished - 2022
EventThirty-First International Joint Conference on Artificial Intelligence - Messe Wien, Vienna, Austria
Duration: 23 Jul 202229 Jul 2022


ConferenceThirty-First International Joint Conference on Artificial Intelligence
Abbreviated titleIJCAI 2022
Internet address


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