Abstractly Interpreting Argumentation Frameworks for Sharpening Extensions

Cycles of attacking arguments pose non-trivial issues in Dung style argumentation theory, apparent behavioural difference between odd and even length cycles being a notable one. While a few methods were proposed for treating them, to - in particular - enable selection of acceptable arguments in an odd-length cycle when Dung semantics could select none, so far the issues have been observed from a purely argument-graph-theoretic perspective. Per contra, we consider argument graphs together with a certain lattice like semantic structure over arguments e.g. ontology. As we show, the semantic-argumentgraphic hybrid theory allows us to apply abstract interpretation, a widely known methodology in static program analysis, to formal argumentation. With this, even where no arguments in a cycle could be selected sensibly, we could say more about arguments acceptability of an argument framework that contains it. In a certain sense, we can verify Dung extensions with respect to a semantic structure in this hybrid theory, to consolidate our confidence in their suitability. By defining the theory, and by making comparisons to existing approaches, we ultimately discover that whether Dung semantics, or an alternative semantics such as cf2, is adequate or problematic depends not just on an argument graph but also on the semantic relation among the arguments in the graph.