On the Correspondence of Non-flat Assumption-based Argumentation and Logic Programming with Negation as Failure in the Head

• URL: http://arxiv.org/abs/2405.09415v3
• Date: Tue, 13 Aug 2024 15:32:51 GMT
• Title: On the Correspondence of Non-flat Assumption-based Argumentation and Logic Programming with Negation as Failure in the Head
• Authors: Anna Rapberger, Markus Ulbricht, Francesca Toni,
• Abstract summary: We show a correspondence between non-flat ABA and LPs with negation as failure in their head. We then extend this result to so-called set-stable ABA semantics, originally defined for the fragment of non-flat ABA called bipolar ABA. We showcase how to define set-stable semantics for LPs with negation as failure in their head and show the correspondence to set-stable ABA semantics.
• Score: 20.981256612743145
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The relation between (a fragment of) assumption-based argumentation (ABA) and logic programs (LPs) under stable model semantics is well-studied. However, for obtaining this relation, the ABA framework needs to be restricted to being flat, i.e., a fragment where the (defeasible) assumptions can never be entailed, only assumed to be true or false. Here, we remove this restriction and show a correspondence between non-flat ABA and LPs with negation as failure in their head. We then extend this result to so-called set-stable ABA semantics, originally defined for the fragment of non-flat ABA called bipolar ABA. We showcase how to define set-stable semantics for LPs with negation as failure in their head and show the correspondence to set-stable ABA semantics.

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