Argumentation Semantics under a Claim-centric View: Properties, Expressiveness and Relation to SETAFs

Claim-augmented argumentation frameworks (CAFs) constitute a generic formalism for conflict resolution of conclusionoriented problems in argumentation. CAFs extend Dung argumentation frameworks (AFs) by assigning a claim to each argument. So far, semantics for CAFs are defined with respect to the underlying AF by interpreting the extensions of the respective AF semantics in terms of the claims of the accepted arguments; we refer to them as inherited semantics of CAFs. A central concept of many argumentation semantics is maximization, which can be done with respect to arguments as in preferred semantics, or with respect to the range as in semi-stable semantics. However, common instantiations of argumentation frameworks require maximality on the claim-level and inherited semantics often fail to provide maximal claim-sets even if the underlying AF semantics yields maximal argument sets. To address this issue, we investigate a different approach and introduce claim-level semantics (cl-semantics) for CAFs where maximization is performed on the claim-level. We compare these two approaches for five prominent semantics (preferred, naive, stable, semistable, and stage) and relate in total eleven CAF semantics to each other. Moreover, we show that for a certain subclass of CAFs, namely well-formed CAFs, the different versions of preferred and stable semantics coincide, which is not the case for the remaining semantics. We furthermore investigate a recently established translation between well-formed CAFs and SETAFs and show that, in contrast to the inherited naive, semi-stable and stage semantics, the cl-semantics correspond to the respective SETAF semantics. Finally, we investigate the expressiveness of the considered semantics in terms of their signatures.

[1]  Phan Minh Dung,et al.  On the Acceptability of Arguments and its Fundamental Role in Nonmonotonic Reasoning, Logic Programming and n-Person Games , 1995, Artif. Intell..

[2]  Thomas Linsbichler,et al.  Characteristics of multiple viewpoints in abstract argumentation , 2014, Artif. Intell..

[3]  Francesca Toni,et al.  An Assumption-Based Framework for Non-Monotonic Reasoning , 1993, LPNMR.

[4]  Anthony Hunter,et al.  Instantiating abstract argumentation with classical logic arguments: Postulates and properties , 2011, Artif. Intell..

[5]  Pietro Baroni,et al.  An introduction to argumentation semantics , 2011, The Knowledge Engineering Review.

[6]  Henry Prakken,et al.  An abstract framework for argumentation with structured arguments , 2010, Argument Comput..

[7]  Simon Parsons,et al.  A Generalization of Dung's Abstract Framework for Argumentation: Arguing with Sets of Attacking Arguments , 2006, ArgMAS.

[8]  Henry Prakken,et al.  Towards Artificial Argumentation , 2017, AI Mag..

[9]  Martin Caminada,et al.  On the equivalence between logic programming semantics and argumentation semantics , 2015, Int. J. Approx. Reason..

[10]  Philippe Besnard,et al.  Logical limits of abstract argumentation frameworks , 2013, J. Appl. Non Class. Logics.

[11]  Stefan Woltran,et al.  On the Relation Between Claim-Augmented Argumentation Frameworks and Collective Attacks , 2020, ECAI.

[12]  Ringo Baumann,et al.  Extension Removal in Abstract Argumentation - An Axiomatic Approach , 2019, AAAI.

[13]  Stefan Woltran,et al.  Complexity of Abstract Argumentation under a Claim-Centric View , 2019, AAAI.

[14]  Martin Caminada,et al.  On the Difference between Assumytion-Based Argumentation and Abstract Argumentation , 2015, FLAP.

[15]  Anna Rapberger.  Defining Argumentation Semantics under a Claim-centric View , 2020, STAIRS@ECAI.

[16]  Martin Caminada,et al.  On the evaluation of argumentation formalisms , 2007, Artif. Intell..