Revision, defeasible conditionals and non-monotonic inference for abstract dialectical frameworks

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

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

For propositional beliefs, there are well-established connections between belief revision, defeasible conditionals, and nonmonotonic inference. In argumentative contexts, such connections have not yet been investigated. On the one hand, the exact relationship between formal argumentation and nonmonotonic inference relations is a research topic that keeps on eluding researchers despite recently intensified efforts, whereas argumentative revision has been studied in numerous works during recent years. In this paper, we show that relationships between belief revision, defeasible conditionals, and nonmonotonic inference similar to those in propositional logic hold in argumentative contexts as well. We first define revision operators for abstract dialectical frameworks, and use such revision operators to define dynamic conditionals by means of the Ramsey test. We show that such conditionals can be equivalently defined using a total preorder over three-valued interpretations, and study the inferential behaviour of the resulting conditional inference relations.
Original languageEnglish
Article number103876
Number of pages33
JournalArtificial Intelligence
Volume317
DOIs
Publication statusPublished - Apr 2023

Keywords

  • Argumentation
  • Belief revision and update
  • belief merging information fusion
  • Nonmonotonic logics
  • default logics
  • conditional logics
  • Abstract dialectical frameworks

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