Preferential Reasoning with Typicality in ASP over Weighted Argumentation Graphs in a Gradual Semantics

Recently some new gradual argumentation semantics have been proposed inspired by a fuzzy multipreferential semantics for weighted conditional knowledge bases with typicality. In this paper we extend these semantics to the finitely-valued case, and develop an ASP approach for conditional reasoning over a weighted argumentation graph, through the verification of graded conditional implications over arguments and over boolean combination of arguments. The semantics defined in the paper is enforced via a custom propagator. The paper also develops a probabilistic semantics for gradual argumentation, which builds on the many-valued conditional semantics.