Heyninck, Jesse and Thimm, Matthias and Kern-Isberner, Gabriele and Rienstra, Tjitze and Skiba, Kenneth (2021) On the Relation between Possibilistic Logic and Abstract Dialectical Frameworks, Proceedings of Proceedings of 19th International Workshop on Non-Monotonic Reasoning, 3-5 November 2021, online.
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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, the question poses itself as to whether some and which monotonic three-valued logic underlies ADFs, in the sense that it allows to capture the main semantic concepts underlying ADFs. As an entry-point for such an investigation, we take the concept of model of an ADF, which was originally formulated on the basis of Kleene’s threevalued logic. We show that an optimal concept of a model arises when instead of Kleene’s three-valued logic, possibilistic logic is used. We then show that in fact, possibilistic logic is the most conservative three-valued logic that fulfils this property, and that possibilistic logic can faithfully encode all other semantical concepts for ADFs. Based on this result, we also make some observations on strong equivalence and introduce possibilistic ADFs.
| Item Type: | Conference paper |
|---|---|
| Subjects: | Computing methodologies > Artificial intelligence > Knowledge representation and reasoning Computing methodologies > Artificial intelligence > Knowledge representation and reasoning > Nonmonotonic, default reasoning and belief revision |
| Date Deposited: | 08 Dec 2021 06:19 |
| Last Modified: | 08 Dec 2021 06:19 |
| URI: | https://pubs.cs.uct.ac.za/id/eprint/1517 |
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