Introducing equational semantics for argumentation networks

Authors:
Dov M. Gabbay
Affiliations:
King's College London and Bar Ilan University Israel and University of Luxembourg
Venue:
ECSQARU'11 Proceedings of the 11th European conference on Symbolic and quantitative approaches to reasoning with uncertainty
Year:
2011

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Abstract

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, etc, etc. The equational approach has its conceptual roots in the 19th century following the algebraic equational approach to logic by George Boole, Louis Couturat and Ernst Schroeder.