On Restricting the Impact of Self-attacking Arguments in Gradual Semantics

The issue of how a semantics should deal with self-attacking arguments was always a subject of debate amongst argumentation scholars. A consensus exists for extension-based semantics because those arguments are always rejected (as soon as the semantics in question respect conflict-freeness). In case of gradual semantics, the question is more complex, since other criteria are taken into account. A way to check the impact of these arguments is to use the principles (i.e. desirable properties to be satisfied by a semantics) from the literature. Principles like Self-Contradiction and Strong Self-Contradiction prescribe how to deal with self-attacking arguments. We show that they are incompatible with the well-known Equivalence principle (which is satisfied by almost all the existing gradual semantics), as well as with some other principles (e.g. Counting). This incompatibility was not studied until now and the class of semantics satisfying Self-Contradiction is under-explored. In the present paper, we explore that class of semantics. We show links and incompatibilities between several principles. We define a semantics that satisfies (Strong) Self-Contradiction and a maximal number of compatible principles. We introduce an iterative algorithm to calculate our semantics and prove that it always converges. We also provide a characterisation of our semantics. Finally, we experimentally show that our semantics is computationally efficient.