Inductive Defense for Sceptical Semantics of Extended Argumentation

An abstract argumentation framework may have many extensions. Which extension should be adopted as the semantics depends on the sceptical attitudes of the reasoners. Different degrees of scepticism lead to different semantics ranging from the grounded extension as the most sceptical semantics to preferred extensions as the least sceptical semantics. Extending abstract argumentation to allow attacks to be attacked, subjects attacks to argumentation and hence gives rise to a new dimension of scepticism for characterizing how sceptically attacks are accepted. In this paper we present a semantics based on the notion of inductive (grounded) defense of attacks which is sceptical towards the acceptance of attacks but credulous towards the acceptance of arguments. We show that the semantics preserves fundamental properties of abstract argumentation including the monotonicity of the characteristic function. We further show that any extension of the semantics proposed by Gabbay; Baroni, Cerutti, Giacomin and Guida1; and Modgil contains a sceptical part being an extension of our semantics, and a credulous part resulted from its credulousness towards the acceptance of attacks. We then introduce a stratified form of extended argumentation which still allows an unbounded number of levels of attacks against attacks while assuring that all proposed semantics coincide. In this paper we also develop a sound and complete dialectical proof procedure for the presented semantics following a model of dispute that alternates between argumentation to accept arguments and to accept attacks. Baroni at al for short.