  Assumption-based argumentation (ABA) is a central structured argumentation
formalism. As shown recently, answer set programming (ASP) enables efficiently
solving NP-hard reasoning tasks of ABA in practice, in particular in the
commonly studied logic programming fragment of ABA. In this work, we harness
recent advances in incremental ASP solving for developing effective algorithms
for reasoning tasks in the logic programming fragment of ABA that are
presumably hard for the second level of the polynomial hierarchy, including
skeptical reasoning under preferred semantics as well as preferential
reasoning. In particular, we develop non-trivial counterexample-guided
abstraction refinement procedures based on incremental ASP solving for these
tasks. We also show empirically that the procedures are significantly more
effective than previously proposed algorithms for the tasks.
  This paper is under consideration for acceptance in TPLP.
