Practical argumentation semantics for socially efficient defeasible consequence

An abstract argumentation framework and the semantics, often called Dungean semantics, give a general framework for nonmonotonic logics. In the last fifteen years, a great number of papers in computational argumentation adopt Dungean semantics as a fundamental principle for evaluating various kinds of defeasible consequences. Recently, many papers address problems not only with theoretical reasoning, i.e., reasoning about what to believe, but also practical reasoning, i.e., reasoning about what to do. This paper proposes a practical argumentation semantics specific to practical argumentation. This is motivated by our hypothesis that consequences of such argumentation should satisfy Pareto optimality because the consequences strongly depend on desires, aims, or values an individual agent or a group of agents has. We define a practical argumentation framework and two kinds of extensions, preferred and grounded extensions, with respect to each group of agents. We show that evaluating Pareto optimality can be translated to evaluating preferred extensions of a particular practical argumentation framework. Furthermore, we show that our semantics is a natural extension of Dungean semantics in terms of considering more than one defeat relation. We give a generality order of four practical argumentation frameworks specified by taking into account Dungean semantics and Pareto optimality. We show that a member of preferred extensions of the most specific one is not just Pareto optimal, but also it is theoretically justified.