Ranking Semantics Based on Subgraphs Analysis

We propose a set of novel ranking-based semantics based on a measure of the sensitivity of each argument in an abstract argumentation framework. The sensitivity index is an indicator of how sensitive the label assigned to an argument by an argumentation semantics is, and it is derived from the topology of the graph via a subgraphs analysis coupled with the postulates of the chosen semantics. Using the total rank on arguments induced by such indicator, we propose two ranking-based semantics. We compare the behaviour of our semantics with recent proposals and a widespread set of properties identified in literature. A key feature of our semantics is that the attack relation between arguments keeps the same meaning as found in Dung's abstract semantics. By still relying on Dung's semantics we can soundly deal with any graph configuration, minimize the addition of ad-hoc postulates and provide a clear interpretation of the ranking of arguments.