Abstract
Abstract The acceptability of attacks plays a key role in defining semantics of higher-order argumentation frameworks (HO-AF). Several approaches have been put forward to describe the recursive acceptability of attacks. The diversity, on the one hand, leads to the variety of HO-AF semantics. However, on the other hand, it also brings difficulties in the formal examination of the relationship among these distinct semantics and the exploration of new semantics. This work aims at exploring the underlying commons in existing HO-AF semantics and examining the role of such commons in the study of HO-AF semantics. To this end, we introduce novel notion of renovation sets to represent the acceptability of attacks, and identify several types of renovation sets for different kinds of acceptability. We then use renovation sets to represent and compare HO-AF semantics built in four different approaches. The proposal of renovation sets provides a general tool for the study of HO-AFs. The representation demonstrates a method of using renovation sets to establish HO-AF semantics. The comparison shows the feasibility of investigating the relationship between different HO-AF semantics with the help of renovation sets.
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