Multi-valued Argumentation Frameworks

In this paper we explore how the seminal Dung’s abstract argumentation framework can be extended to handle arguments containing gradual concepts. We allow arguments to have a degree of truth associated with them and we investigate the degree of truth to which each argument can be considered accepted, rejected and undecided by an abstract argumentation semantics. We propose a truth-compositional recursive computation, and we discuss examples using the major multi-valued logics such as Godel’s, Zadeh’s and Łukasiewicz's logic. The findings are a contribution in the field of non-monotonic approximate reasoning and they also represent a well-grounded proposal towards the introduction of gradualism in argumentation systems.