Dung's Argumentation is Essentially Equivalent to Classical Propositional Logic with the Peirce-Quine Dagger

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 ¬,∧,∨,→ 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. Mathematics Subject Classification (2010). 03B05, 03B22, 03B47, 03B99.