Equational approach to argumentation networks

D. M. Gabbay

Research output: Contribution to journalArticlepeer-review

70 Scopus citations


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.

Original languageEnglish
Pages (from-to)87-142
Number of pages56
JournalArgument and Computation
Issue number2-3
StatePublished - 1 Sep 2012


  • argumentation networks
  • equational approach
  • higher level attacks
  • numerical argumentation
  • support in argumentation
  • time-dependent networks


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