Possibilistic Logic Underlies Abstract Dialectical Frameworks

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

IJCAI 2022poster4 citations

Possibilistic Logic Underlies Abstract Dialectical Frameworks

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

Abstract

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.

Knowledge Representation and Reasoning: ArgumentationKnowledge Representation and Reasoning: Non-monotonic Reasoning

BibTeX

@inproceedings{ijcai2022p368,
  title     = {Possibilistic Logic Underlies Abstract Dialectical Frameworks},
  author    = {Heyninck, Jesse and Kern-Isberner, Gabriele and Rienstra, Tjitze and Skiba, Kenneth and Thimm, Matthias},
  booktitle = {Proceedings of the Thirty-First International Joint Conference on
               Artificial Intelligence, {IJCAI-22}},
  publisher = {International Joint Conferences on Artificial Intelligence Organization},
  editor    = {Lud De Raedt},
  pages     = {2655--2661},
  year      = {2022},
  month     = {7},
  note      = {Main Track},
  doi       = {10.24963/ijcai.2022/368},
  url       = {https://doi.org/10.24963/ijcai.2022/368},
}