A formal characterization of the outcomes of rule-based argumentation systems

Rule-based argumentation systems are developed for reasoning about defeasible information. As a major feature, their logical language distinguishes between strict rules (encoding strict information) and defeasible rules (describing general behavior with exceptional cases). They build arguments by chaining such rules, define attacks between them, use a semantics for evaluating the arguments and finally identify the plausible conclusions that follow from the rules. Focusing on the family of inconsistency-based attack relations, this paper presents the first study of the outcomes of such systems under various acceptability semantics, namely naive, stable, semi-stable, preferred, grounded and ideal. It starts by extending the existing list of rationality postulates that any rule-based system should satisfy. Then, it defines the key notion of option of a theory (a theory being a set of facts, a set of strict rules and a set of defeasible rules). For each of the cited semantics, it characterizes the extensions of a rule-based system that satisfies all the postulates in terms of options of the theory under which the system is built. It also fully characterizes the set of plausible conclusions of the system. The results show that designing a rule-based argumentation system requires great care.