Dialectical Proofs Accounting for Strength of Attacks in Argumentation Systems

We consider argumentation systems taking into account several attack relations of different strength. We focus on the impact of various strength attacks on the semantics of such systems, and particularly on the decision problem of credulous acceptance: namely, focussing on one particular argument, a classical issue is to compute a proof, under the form of an admissible set containing this argument. Taking into account attacks of various strength leads to search for the best proofs.