Characteristics of multiple viewpoints in abstract argumentation

The study of extension-based semantics within the seminal abstract argumentation model of Dung has largely focused on definitional, algorithmic and complexity issues. In contrast, matters relating to comparisons of representational limits, in particular, the extent to which given collections of extensions are expressible within the formalism, have been under-developed. As such, little is known concerning conditions under which a candidate set of subsets of arguments are "realistic" in the sense that they correspond to the extensions of some argumentation framework AF for a semantics of interest. In this paper we present a formal basis for examining extension-based semantics in terms of the sets of extensions that these may express within a single AF. We provide a number of characterization theorems which guarantee the existence of AFs whose set of extensions satisfy specific conditions and derive preliminary complexity results for decision problems that require such characterizations.

[1]  Pietro Baroni,et al.  SCC-recursiveness: a general schema for argumentation semantics , 2005, Artif. Intell..

[2]  Sébastien Konieczny,et al.  On the Revision of Argumentation Systems: Minimal Change of Arguments Statuses , 2014, KR.

[3]  Thomas Linsbichler,et al.  Resolution-Based Grounded Semantics Revisited , 2014, COMMA.

[4]  Paul E. Dunne,et al.  The computational complexity of ideal semantics , 2009, Artif. Intell..

[5]  Stefan Woltran,et al.  Complexity of semi-stable and stage semantics in argumentation frameworks , 2010, Inf. Process. Lett..

[6]  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..

[7]  Richard Chang,et al.  On computing Boolean connectives of characteristic functions , 1995, Mathematical systems theory.

[8]  Ringo Baumann.  What Does it Take to Enforce an Argument? Minimal Change in abstract Argumentation , 2012, ECAI.

[9]  Stefan Woltran,et al.  On the Intertranslatability of Argumentation Semantics , 2011, J. Artif. Intell. Res..

[10]  Yannis Dimopoulos,et al.  Graph Theoretical Structures in Logic Programs and Default Theories , 1996, Theor. Comput. Sci..

[11]  Trevor J. M. Bench-Capon,et al.  COMPUTATIONAL MODELS OF ARGUMENT, PROCEEDINGS OF COMMA 2008 , 2008, COMMA 2008.

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

[13]  Trevor J. M. Bench-Capon,et al.  Argumentation in artificial intelligence , 2007, Artif. Intell..

[14]  Pietro Baroni,et al.  On principle-based evaluation of extension-based argumentation semantics , 2007, Artif. Intell..

[15]  Hannes Strass,et al.  Compact Argumentation Frameworks , 2014, ECAI.

[16]  Pietro Baroni,et al.  On the resolution-based family of abstract argumentation semantics and its grounded instance , 2011, Artif. Intell..

[17]  Wolfgang Dvo.  Comparing the Expressiveness of Argumentation Semantics , 2015 .

[18]  Stefan Woltran,et al.  Abstract Dialectical Frameworks , 2010, KR.

[19]  Bart Verheij,et al.  Two Approaches to Dialectical Argumentation: Admissible Sets and Argumentation Stages , 1999 .

[20]  Guillermo Ricardo Simari,et al.  On the evolving relation between Belief Revision and Argumentation , 2011, The Knowledge Engineering Review.

[21]  Ringo Baumann,et al.  Expanding Argumentation Frameworks: Enforcing and Monotonicity Results , 2010, COMMA.

[22]  Paul E. Dunne,et al.  Semi-stable semantics , 2006, J. Log. Comput..

[23]  Sjur Dyrkolbotn.  How to Argue for Anything: Enforcing Arbitrary Sets of Labellings using AFs , 2014, KR.

[24]  Iyad Rahwan,et al.  Quantifying disagreement in argument-based reasoning , 2012, AAMAS.

[25]  Dov M. Gabbay,et al.  A Logical Account of Formal Argumentation , 2009, Stud Logica.

[26]  Philippe Besnard,et al.  Characterization of Semantics for Argument Systems , 2004, KR.

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

[28]  Trevor J. M. Bench-Capon,et al.  Coherence in finite argument systems , 2002, Artif. Intell..

[29]  Hannes Strass,et al.  On the Maximal and Average Numbers of Stable Extensions , 2013, TAFA.

[30]  Ringo Baumann,et al.  Splitting an Argumentation Framework , 2011, LPNMR.

[31]  Theo Tryfonas,et al.  Frontiers in Artificial Intelligence and Applications , 2009 .