The role of metalanguage in graded logical approaches

This paper is an attempt to show how the metalanguage is important in building a logic dealing with uncertainties. We shall address this issue from two different angles. In one we shall propose a new way to look at the notion of consequence by introducing a series of metalogical notions based on the metalanguage and its interpretation; and in the other we shall present concrete systems of graded logic, which are generated based on both the object language, metalanguage, and their interrelations.