Equivalence in Argumentation Frameworks with a Claim-Centric View – Classical Results with Novel Ingredients

Proceedings of the Nineteenth International Conference on Principles of Knowledge Representation and Reasoning

2022

Self Cite

In this paper we contribute to the investigation of dynamics in assumption-based argumentation (ABA) and investigate situations where a given knowledge base undergoes certain changes. We show that two frequently investigated problems, namely enforcement of a given target atom and deciding strong equivalence of two given ABA frameworks, are intractable in general. Interestingly, these problems are both tractable for abstract argumentation frameworks (AFs) which admit a close correspondence to ABA by constructing semantics-preserving instances. Inspired by this observation, we search for tractable fragments for ABA frameworks by means of the instantiated AFs. We argue that the usual instantiation procedure is not suitable for the investigation of dynamic scenarios since too much information is lost when constructing the AF. We thus consider an extension of AFs, called cvAFs, equipping arguments with conclusions and vulnerabilities in order to better anticipate their role after the underlying knowledge base is extended. We investigate enforcement and strong equivalence for cvAFs and present syntactic conditions to decide them. We show that the correspondence between cvAFs and ABA frameworks is close enough to capture ABA also in dynamic scenarios. This yields the desired tractable ABA fragment. We furthermore discuss consequences for the corresponding problems for logic programs.

Section: Discussionmentioning

confidence: 99%

On Dynamics in Structured Argumentation Formalisms

Proceedings of the Nineteenth International Conference on Principles of Knowledge Representation and Reasoning

2022

Self Cite

“…The present paper is an extended version of the conference version (Baumann, Rapberger, & Ulbricht, 2022). Besides providing full proofs and a stronger intuition about our technical details, the present version extends the previous conference publication by a comprehensive analysis of the equivalence behavior of well-formed CAFs: we present novel results regarding ordinary and strong equivalence, and strong equivalence up to argument renaming for this important sub-class.…”

Section: Introductionmentioning

confidence: 73%

Equivalence in Argumentation Frameworks with a Claim-centric View: Classical Results with Novel Ingredients

Baumann

2023

jair

A common feature of non-monotonic logics is that the classical notion of equivalence does not preserve the intended meaning in light of additional information. Consequently, the term strong equivalence was coined in the literature and thoroughly investigated. In the present paper, the knowledge representation formalism under consideration is claimaugmented argumentation frameworks (CAFs) which provide a formal basis to analyze conclusion-oriented problems in argumentation by adapting a claim-focused perspective. CAFs extend Dung AFs by associating a claim to each argument representing its conclusion. In this paper, we investigate both ordinary and strong equivalence in CAFs. Thereby, we take the fact into account that one might either be interested in the actual arguments or their claims only. The former point of view naturally yields an extension of strong equivalence for AFs to the claim-based setting while the latter gives rise to a novel equivalence notion which is genuine for CAFs. We tailor, examine and compare these notions and obtain a comprehensive study of this matter for CAFs. We conclude by investigating the computational complexity of naturally arising decision problems.

“…Both strong equivalence and enforcement have received increasing attention in the realm of abstract argumentation (Baumann, 2012b;Baumann, Rapberger, & Ulbricht, 2022;Oikarinen & Woltran, 2011). There are, however, only few studies on the aforementioned problems in structured argumentation.…”

Section: Introductionmentioning

confidence: 99%

On Dynamics in Structured Argumentation Formalisms

2023

jair

This paper is a contribution to the research on dynamics in assumption-based argumentation (ABA). We investigate situations where a given knowledge base undergoes certain changes. We show that two frequently investigated problems, namely enforcement of a given target atom and deciding strong equivalence of two given ABA frameworks, are intractable in general. Notably, these problems are both tractable for abstract argumentation frameworks (AFs) which admit a close correspondence to ABA by constructing semanticspreserving instances. Inspired by this observation, we search for tractable fragments for ABA frameworks by means of the instantiated AFs. We argue that the usual instantiation procedure is not suitable for the investigation of dynamic scenarios since too much information is lost when constructing the abstract framework. We thus consider an extension of AFs, called cvAFs, equipping arguments with conclusions and vulnerabilities in order to better anticipate their role after the underlying knowledge base is extended. We investigate enforcement and strong equivalence for cvAFs and present syntactic conditions to decide them. We show that the correspondence between cvAFs and ABA frameworks is close enough to capture dynamics in ABA. This yields the desired tractable fragment. We furthermore discuss consequences for the corresponding problems for logic programs.