A many-valued multi-preferential propositional typicality logic and a conditional interpretation for gradual argumentation

In this paper we develop a many-valued and multi-preferential conditional logic with typicality, based on a multi-preferential semantics, which generalizes KLM preferential semantics. We then exploit the multi-preferential semantics to provide preferential interpretation of gradual argumentation. The approach allows for conditional reasoning over arguments and boolean combination of arguments, with respect to some chosen gradual semantics, through the verification of graded (strict or defeasible) implications over an argumentation graph. The paper also develops a probabilistic semantics for gradual argumentation, which builds on the many-valued semantics.