Two forms of minimality in ASPIC+

Many systems of structured argumentation explicitly require that the facts and rules that make up the argument for a conclusion be the minimal set required to derive the conclusion. ASPIC+ does not place such a requirement on arguments, instead requiring that every rule and fact that are part of an argument be used in its construction. Thus ASPIC+ arguments are minimal in the sense that removing any element of the argument would lead to a structure that is not an argument. In this brief note we discuss these two types of minimality and show how the first kind of minimality can, if desired, be recovered in ASPIC+.

On the links between argumentation-based reasoning and nonmonotonic reasoning

In this paper we investigate the links between instantiated argumentation systems and the axioms for non-monotonic reasoning described in [9] with the aim of characterising the nature of argument based reasoning. In doing so, we consider two possible interpretations of the consequence relation, and describe which axioms are met by ASPIC+ under each of these interpretations. We then consider the links between these axioms and the rationality postulates. Our results indicate that argument based reasoning as characterised by ASPIC+ is - according to the axioms of [9] - non-cumulative and non-monotonic, and therefore weaker than the weakest non-monotonic reasoning systems they considered possible. This weakness underpins ASPIC+'s success in modelling other reasoning systems, and we conclude by considering the relationship between ASPIC+ and other weak logical systems.