Equilibrium States in Numerical Argumentation Networks

Given an argumentation network with initial values to the arguments, we look for algorithms which can yield extensions compatible with such initial values. We find that the best way of tackling this problem is to offer an iteration formula that takes the initial values and the attack relation and iterates a sequence of intermediate values that eventually converges leading to an extension. The properties surrounding the application of the iteration formula and its connection with other numerical and non-numerical techniques proposed by others are thoroughly investigated in this paper.

[1]  Serena Villata,et al.  Changing One's Mind: Erase or Rewind? , 2011, IJCAI.

[2]  D. M. Gabbaya.  Equational approach to argumentation networks , 2012 .

[3]  Anthony Hunter,et al.  A logic-based theory of deductive arguments , 2001, Artif. Intell..

[4]  Serena Villata,et al.  Changing One ’ s Mind : Erase or Rewind ? Possibilistic Belief Revision with Fuzzy Argumentation based on Trust , 2011 .

[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]  J. Meza.  Newton's method , 2011 .

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

[8]  João Leite,et al.  Extending Social Abstract Argumentation with Votes on Attacks , 2013, TAFA.

[9]  Martin Caminada.  A labelling approach for ideal and stage semantics , 2011, Argument Comput..

[10]  Martin Caminada.  An Algorithm for Computing Semi-stable Semantics , 2007, ECSQARU.

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

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

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

[14]  Dov M. Gabbay,et al.  A Numerical Approach to the Merging of Argumentation Networks , 2012, CLIMA.

[15]  Dov M. Gabbay,et al.  An equational approach to the merging of argumentation networks , 2014, J. Log. Comput..

[16]  Gabriella Pigozzi,et al.  On judgment aggregation in abstract argumentation , 2009, Autonomous Agents and Multi-Agent Systems.

[17]  Claudette Cayrol,et al.  Graduality in Argumentation , 2011, J. Artif. Intell. Res..

[18]  João Leite,et al.  Social Abstract Argumentation , 2011, IJCAI.

[19]  E. Süli,et al.  An introduction to numerical analysis , 2003 .

[20]  M. Hassell.  The dynamics of arthropod predator-prey systems. , 1979, Monographs in population biology.

[21]  Dov M. Gabbay,et al.  Probabilistic Argumentation: An Equational Approach , 2015, Logica Universalis.

[22]  Dov M. Gabbay.  Introducing Equational Semantics for Argumentation Networks , 2011, ECSQARU.