AGM Meets Abstract Argumentation: Expansion and Revision for Dung Frameworks

In this paper we combine two of the most important areas of knowledge representation, namely belief revision and (abstract) argumentation. More precisely, we show how AGM-style expansion and revision operators can be defined for Dung's abstract argumentation frameworks (AFs). Our approach is based on a reformulation of the original AGM postulates for revision in terms of monotonic consequence relations for AFs. The latter are defined via a new family of logics, called Dung logics, which satisfy the important property that ordinary equivalence in these logics coincides with strong equivalence for the respective argumentation semantics. Based on these logics we define expansion as usual via intersection of models. We show the existence of such operators. This is far from trivial and requires to study realizability in the context of Dung logics. We then study revision operators. We show why standard approaches based on a distance measure on models do not work for AFs and present an operator satisfying all postulates for a specific Dung logic.

[1]  Miroslaw Truszczynski,et al.  Strong and uniform equivalence of nonmonotonic theories – an algebraic approach , 2006, Annals of Mathematics and Artificial Intelligence.

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

[3]  Victor Marek.  Introduction to Mathematics of Satisfiability , 2009 .

[4]  Claudette Cayrol,et al.  Change in Abstract Argumentation Frameworks: Adding an Argument , 2010, J. Artif. Intell. Res..

[5]  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..

[6]  Hannes Strass,et al.  Abstract Dialectical Frameworks Revisited , 2013, IJCAI.

[7]  Mukesh Dalal,et al.  Investigations into a Theory of Knowledge Base Revision , 1988, AAAI.

[8]  Sanjay Modgil,et al.  Reasoning about preferences in argumentation frameworks , 2009, Artif. Intell..

[9]  Marianne Winslett,et al.  Reasoning about Action Using a Possible Models Approach , 1988, AAAI.

[10]  Ringo Baumann,et al.  Metalogical Contributions to the Nonmonotonic Theory of Abstract Argumentation , 2014 .

[11]  Stefan Woltran,et al.  The role of self-attacking arguments in characterizations of equivalence notions , 2016, J. Log. Comput..

[12]  Mary-Anne Williams,et al.  Transmutations of Knowledge Systems , 1994, KR.

[13]  Ringo Baumann,et al.  Infinite Argumentation Frameworks - On the Existence and Uniqueness of Extensions , 2015, Advances in Knowledge Representation, Logic Programming, and Abstract Argumentation.

[14]  Pietro Baroni,et al.  Semantics of Abstract Argument Systems , 2009, Argumentation in Artificial Intelligence.

[15]  Ken Satoh.  Nonmonotonic Reasoning by Minimal Belief Revision , 1988, FGCS.

[16]  Grigoris Antoniou,et al.  A Strategy for Revising Default Theory Extensions , 1998, International Conference on Principles of Knowledge Representation and Reasoning.

[17]  Sébastien Konieczny,et al.  A Translation-Based Approach for Revision of Argumentation Frameworks , 2014, JELIA.

[18]  John Fox,et al.  The Knowledge Engineering Review , 1984, The Knowledge Engineering Review.

[19]  Guilin Qi,et al.  A Survey of Revision Approaches in Description Logics , 2008, Description Logics.

[20]  Ringo Baumann,et al.  Context-free and Context-sensitive Kernels: Update and Deletion Equivalence in abstract Argumentation , 2014, ECAI.

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

[22]  Peter Aczel etc.  HANDBOOK OF MATHEMATICAL LOGIC , 1999 .

[23]  Ringo Baumann,et al.  Analyzing the Equivalence Zoo in Abstract Argumentation , 2013, CLIMA.

[24]  Brian A. Davey,et al.  An Introduction to Lattices and Order , 1989 .

[25]  James P. Delgrande,et al.  Belief revision in Horn theories , 2015, Artif. Intell..

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

[27]  Peter Gärdenfors,et al.  On the logic of theory change: Partial meet contraction and revision functions , 1985, Journal of Symbolic Logic.

[28]  Stefan Woltran,et al.  Characterizing Strong Equivalence for Argumentation Frameworks , 2010, KR.

[29]  Stefan Woltran,et al.  AGM-Style Belief Revision of Logic Programs under Answer Set Semantics , 2008, LPNMR.