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. (shrink)

In this paper we show that some versions of Dung’s abstract argumentation frames are equivalent to classical propositional logic. In fact, Dung’s attack relation is none other than the generalised Peirce–Quine dagger connective of classical logic which can generate the other connectives ${\neg, \wedge, \vee, \to}$ of classical logic. After establishing the above correspondence we offer variations of the Dung argumentation frames in parallel to variations of classical logic, such as resource logics, predicate logic, etc., etc., and create resource argumentation (...) frames, predicate argumentation frames, etc., etc. We also offer the notion of logic proof as a geometrical walk along the nodes of a Dung network and thus we are able to offer a geometrical abstraction of the notion of inference based argumentation. Thus our paper is also a contribution to the question: “What is a logical system” in as much as it integrates logic with abstract argumentation networks. (shrink)

argumentation has been shown to be a powerful tool within many fields such as artificial intelligence, logic and legal reasoning. In this paper we enhance Dung’s well-known abstract argumentation framework with explanatory capabilities. We show that an explanatory argumentation framework (EAF) obtained in this way is a useful tool for the modeling of scientific debates. On the one hand, EAFs allow for the representation of explanatory and justificatory arguments constituting rivaling scientific views. On the other hand, different procedures for selecting (...) arguments, corresponding to different methodological and epistemic requirements of theory evaluation, can be formulated in view of our framework. (shrink)

1. Argumentation, by considering arguments and their interactions, is a way of reasoning that has proven successful in many contexts, for instance, in multi-agent applications (Carrera & Iglesias,...