A credulous semantics of higher-order argumentation frameworks based on credulously accepted attacks

As a useful reasoning model, higher-order argumentation frameworks (HO-AF) have been studied in many works. This paper contributes to the theory of HO-AFs in three aspects. First, the acceptability of attacks depending on a set of argument is explored, and credulously accepted attacks w.r.t. a set of arguments are formally characterised by introducing regular renovation sets. Second, a new semantics, named regular semantics (r-semantics) is established for HO-AFs. Every complete (or conflict-free, admissible) set in Modgil's semantics is complete (or conflict-free, admissible) in r-semantics. Some maximality-based r-semantics are just the argument part of the corresponding semantics of Baroni et al. Third, an efficient method is put forward to calculate these maximality-based Baroni's semantics through r-semantics.