Abstract rule-based argumentation

This chapter reviews abstract rule-based approaches to argumentation, in particular the ASPIC + framework. In ASPIC + and its predecessors, going back to the seminal work of John Pollock, arguments can be formed by combining strict and defeasible inference rules and conflicts between arguments can be resolved in terms of a preference relation on arguments. This results in abstract argumentation frameworks (a set of arguments with a binary relation of defeat), so that arguments can be evaluated with the theory of abstract argumentation. First the basic ASPIC + framework is reviewed, possible ways to instantiate it are discussed and how these instantiations can satisfy closure and consistency properties. Then the relation between ASPIC + and other work in formal argumentation and nonmonotonic logic is discussed, including a review of how other approaches can be reconstructed as instantiations of ASPIC +. Further developments and variants of the basic ASPIC + framework are also reviewed, including developments with alternative or generalised notions of attack and defeat and variants with further constraints on arguments. Finally, implementations and applications of ASPIC + are briefly reviewed and some open problems and avenues for further research are discussed.