Relative Truth Degree of Logic Formulas and Graded Fuzzy Logic

The concept of logic proposition induced functions is proposed in the present paper, then the concept of relative truth degree of propositions with respect to a logic theory r is introduced by means of infinite product of evenly distributed probability spaces and integrated semantics respectively w.r.t. discrete and continuous situations, and a graded approximate reasoning theory is established. Next, theory of consistency degrees of finite logic theories is also proposed. Finally, the simple application of graded fuzzy logic in fuzzy inference is given by examples.