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.
