Based on △ deduction theorem and true value distribution, this paper proves true value relationship theorem of valid inference in △ fuzzy logic system SBL ~ with involutive negation. Secondly, as an example of axiomatic extensions of SBL ~ system, Godel ~ is quantified by introducing △ similarity and △ distance. Then the paper proves the continuity of logic operators→,~by using the true value relationship theorem, gives the method to calculate the distance between the formula and theory. Finally, this paper proposes three different types of approximate reasoning patterns and discusses the relationships between three modes in Godel ~ .