An intrinsic fuzzy set on the universe of discourse of predicate formulas

We construct and study a new intrinsic fuzzy subset τ on the crisp set F of all first-order logic formulas in two-valued logic. In order to define this fuzzy set, we need to introduce a number of other new concepts, such as the relative satisfiability degree, the least and the largest interpretations, and the average validity degree of a formula. One of the main results proved in this paper is that all the membership degrees of this fuzzy set form a dense subset of [0,1]. This new intrinsic fuzzy set will be used to develop a kind of fuzzy deductive reasoning of Pavelka's type.