Preferences and Unrestricted Rebut

The work of Caminada & Amgoud presents two possible ways of satisfying the rationality postulates: one using restricted rebut, and one using unrestricted rebut. Subsequent work on ASPIC+ has extended the work of Caminada & Amgoud, for instance by allowing preferences over arguments. However, such extensions have utilised restricted rebut only. In the current paper, we make the case for unrestricted rebut, and provide a formalism (called ASPIC−) that implements preferences between the defeasible rules, in the context of unrestricted rebut while still satisfying the rationality postulates of Caminada & Amgoud.