Weakly Complete Semantics Based on Undecidedness Blocking

In this paper we introduce a novel family of semantics called weakly complete semantics. Differently from Dung's complete semantics, weakly complete semantics employs a mechanism called undecidedness blocking by which the label undecided of an attacking argument is not always propagated to an otherwise accepted attacked argument. The new semantics are conflict-free, non-admissible but employing a weaker notion of admissibility; they allow reinstatement and they retain the majority of properties of complete semantics. We show how both weakly complete and Dung's complete semantics can be generated by applying different undecidedness blocking strategies, making undecidedness blocking a unifying mechanism underlying argumentation semantics. The semantics are also an example of ambiguity blocking Dunganian semantics and the first semantics to tackle the problem of self-defeating attacking arguments. In the last part of the paper we compare weakly complete semantics with the recent work of Baumann et al. on weakly admissible semantics. Since the two families of semantics do not coincide, a principle-based analysis of the two approaches is provided. The analysis shows how our semantics satisfy a number of principles satisfied by Dung's complete semantics but not by Baumann et al. semantics, including directionality, abstention, SCC-decomposability and cardinality of extensions, making them a more faithful non-admissible version of Dung' semantics.