Thesis for the degree of Master of Science Relating proof standards and abstract argumentation

The basic idea of argumentation is to construct arguments in favour of and against a certain statement, selecting the acceptable arguments, and in the end determining which statements hold. To explain how arguments defend their position, they can be structured by their used knowledge and rules. Several approaches to structured argumentation have been developed and subsequently related through a single framework called ASPIC. Although the theoretical relations between these approaches have thus been clarified, there have been significant developments in structured argumentation that deviate from this approach. Carneades is a recently proposed formalism for structured argumentation with varying proof standards, inspired by legal reasoning but more generally applicable. Its distinctive feature is that each statement can be given its own proof standard, which is claimed to allow a more natural account of reasoning under burden of proof than existing formalisms for structured argumentation, in which proof standards are defined globally. However, its relation with Dung’s seminal abstract approach to argumentation is still an open question. In this thesis the two formalisms are formally related by translating Carneades into ASPIC. Since ASPIC is defined to generate Dung-style abstract argumentation frameworks, this in effect translates Carneades graphs into abstract argumentation frameworks. For this translation, we prove a formal correspondence and show that certain rationality postulates hold. It is furthermore proven that Carneades always induces a unique Dung extension, which is the same in all of Dung’s semantics, allowing us to generalise Carneades to cycle-containing structures.