Approximate Reasoning in Godel 4-Valued Nonlinear Ordered Set Logic System

In order to establish approximate reasoning in 4-value nonlinear ordered set logic system, firstly we define the truth degree of formula in 4-valued nonlinear ordered set using the infinite product of probability space with potency is 4, then give the inference rules based on truth degree. Furthermore, we prove that the set of truth degree of all formulas in the range of [0, 1] is dense and give the general expression of the set of truth degree in Godel 4-valued nonlinear ordered set logic system. Finally, we define similarity degree between formulas and a kind of pseudo-distance in the set of all formulas, so provide a possible structure of approximate reasoning theory.