The computational complexity of ideal semantics Original Research Article

We analyse the computational complexity of the recently proposed ideal semantics within both abstract argumentation frameworks (afs) and assumption-based argumentation frameworks (abfs). It is shown that while typically less tractable than credulous admissibi-lity semantics, the natural decision problems arising with this extension-based model can, perhaps surprisingly, be decided more efficiently than sceptical preferred semantics. In particular the task of finding the unique ideal extension is easier than that of deciding if a given argument is accepted under the sceptical semantics. We provide efficient algorithmic approaches for the class of bipartite argumentation frameworks and, finally, present a number of technical results which offer strong indications that typical problems in ideal argumentation are complete for the class image of languages decidable by polynomial time algorithms allowed to make non-adaptive queries to a image oracle, where image is an upper bound on the computational complexity of deciding credulous acceptance: image for afs and logic programming (lp) instantiations of abfs; image for abfs modelling default theories.