Stage semantics and the SCC-recursive schema for argumentation semantics
Wolfgang Dvořák, Sarah Alice Gaggl · Journal of Logic and Computation · 2014
Recently, stage and cf 2 semantics for abstract argumentation attracted specific attention. By distancing from the notion of defence, they are capable to select arguments out of odd-length cycles. In case of cf 2 semantics, the SCC-recursive schema guarantees that important evaluation criteria for argumentation semantics, like directionality, weak- and CF -reinstatement, are fulfilled. Beside several desirable properties, both stage and cf 2 semantics still have some drawbacks. The stage semantics does not satisfy the above mentioned evaluation criteria, whereas cf 2 semantics produces some questionable results on frameworks with cycles of length ≥ 6. Therefore, we suggest to combine stage semantics with the SCC-recursive schema of cf 2 semantics. The resulting stage 2 semantics overcomes the problems regarding cf 2 and stage semantics. We study properties of stage 2 semantics and its relations to existing semantics, show that it fulfills the mentioned evaluation criteria, study strong equivalence for stage 2 semantics and provide a comprehensive complexity analysis of the associated reasoning problems. Besides the analysis of stage 2 semantics, we also complement existing complexity results for cf 2 by an analysis of tractable fragments and fixed parameter tractability. Furthermore, we provide answer-set programming (ASP) encodings for stage 2 semantics and labelling-based algorithms for cf 2 and stage 2 semantics.