Abstract: In recent years,formal argumentation has gradually become one of the research hotspots in the field of artificial intelligence.Since Dung put forward the abstract argumentation framework in 1995,it is generally accepted in the academic circles that the core task of argumentation is to evaluate a set of arguments under various extension-based semantics,so as to determine their justification status.Graded argumentation system(GAS) is a generalization of the classical Dung-style Argumentation System (DAS),which provides a more fine-grained notion of argument status by generalizing the two core principles of DAS semantics,conflict-free and acceptability.The current research on semantic equivalence of argumentation system mainly focuses on the framework and argument level,which can provide powerful support for its structural reduction.For the semantic equivalence of the arguments in two different graded argumentation systems,firstly,fragments of the graded argumentation system are formalized by using Graded Modal Logic (GML).Then,the one-to-one correspondence between the extension-based semantics and GML formula in graded argumentation system is established and proved.Finally,the graded bisimulation relation is defined and that it implies four prominent semantic equivalences of GAS is proved.

Key words: DAS, Formal argumentation, GML, Graded argumentation system, Graded bisimulation