Paracoherent Answer Set Semantics meets Argumentation Frameworks
This work addresses a theoretical limitation in abstract argumentation for AI researchers, but it is incremental as it builds on existing semantics without major breakthroughs.
The paper tackles the problem of incoherent argumentation frameworks (AFs) that lack stable extensions by introducing paracoherent extensions, which are derived from paracoherent answer set semantics, and shows that this approach maintains computational costs and symmetric behavior compared to existing semantics like semi-stable and stage.
In the last years, abstract argumentation has met with great success in AI, since it has served to capture several non-monotonic logics for AI. Relations between argumentation framework (AF) semantics and logic programming ones are investigating more and more. In particular, great attention has been given to the well-known stable extensions of an AF, that are closely related to the answer sets of a logic program. However, if a framework admits a small incoherent part, no stable extension can be provided. To overcome this shortcoming, two semantics generalizing stable extensions have been studied, namely semi-stable and stage. In this paper, we show that another perspective is possible on incoherent AFs, called paracoherent extensions, as they have a counterpart in paracoherent answer set semantics. We compare this perspective with semi-stable and stage semantics, by showing that computational costs remain unchanged, and moreover an interesting symmetric behaviour is maintained. Under consideration for acceptance in TPLP.