Equational approach to argumentation networks

This paper provides equational semantics for Dung’s argumentation networks. The network nodes get numerical values in [0,1], and are supposed to satisfy certain equations. The solutions to these equations correspond to the “extensions” of the network. This approach is very general and includes the Caminada labelling as a special case, as well as many other so-called network extensions, support systems, higher level attacks, Boolean networks, dependence on time, and much more. The equational approach has its conceptual roots in the nineteenth century following the algebraic equational approach to logic by George Boole, Louis Couturat, and Ernst Schroeder.

[1]  Trevor J. M. Bench-Capon.  Persuasion in Practical Argument Using Value-based Argumentation Frameworks , 2003, J. Log. Comput..

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

[3]  Dov M. Gabbay,et al.  Temporal Dynamics of Support and Attack Networks: From Argumentation to Zoology , 2005, Mechanizing Mathematical Reasoning.

[4]  Sanjay Modgil,et al.  An Abstract Theory of Argumentation That Accommodates Defeasible Reasoning About Preferences , 2007, ECSQARU.

[5]  Dov M. Gabbay,et al.  Fibring Argumentation Frames , 2009, Stud Logica.

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

[7]  Dov M. Gabbay,et al.  Logical Modes of Attack in Argumentation Networks , 2009, Stud Logica.

[8]  Pietro Baroni,et al.  Encompassing Attacks to Attacks in Abstract Argumentation Frameworks , 2009, ECSQARU.

[9]  Dov M. Gabbay,et al.  Complete Extensions in Argumentation Coincide with 3-Valued Stable Models in Logic Programming , 2009, Stud Logica.

[10]  Dov M. Gabbay,et al.  Annotation Theories over Finite Graphs , 2009, Stud Logica.

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

[12]  Claudette Cayrol,et al.  Coalitions of arguments: A tool for handling bipolar argumentation frameworks , 2010, Int. J. Intell. Syst..

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

[14]  Serena Villata,et al.  Support in Abstract Argumentation , 2010, COMMA.

[15]  Phan Minh Dung,et al.  Inductive Defense for Sceptical Semantics of Extended Argumentation , 2011, J. Log. Comput..

[16]  Adina Magda Florea,et al.  Fuzzy Labeling for Argumentation Frameworks , 2011, ArgMAS.

[17]  Pietro Baroni,et al.  Computing with Infinite Argumentation Frameworks: The Case of AFRAs , 2011, TAFA.

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

[19]  Dov M. Gabbay.  Dung’s Argumentation is Essentially Equivalent to Classical Propositional Logic with the Peirce–Quine Dagger , 2011, Logica Universalis.

[20]  Martin Caminada,et al.  On the Limitations of Abstract Argumentation , 2011 .

[21]  H. Barringera,et al.  Temporal , numerical and meta-level dynamics in argumentation networks , 2012 .

[22]  Dov M. Gabbay,et al.  What Is Negation as Failure? , 2012, Logic Programs, Norms and Action.

[23]  Dov M. Gabbay.  The Equational Approach to CF2 Semantics , 2012, COMMA.

[24]  Dov M. Gabbay,et al.  Modal and temporal argumentation networks , 2012, Argument Comput..