On Quantified Axiomatic Extension System Of G?del By Adding New Operators

By adding new operator ? in G(?)del n-valued propositional logic system,? truth degree of propositional formulas and it's equivalent form are given,some basic properties such as MP and HS rules are proved.By adding new operators ? and ~,axiomatic extension of G(?)del n-valued propositional logic system is introduced,which is denoted as G(?)del~,?.The concepts of t truth degree,t similarity degree and t pseudo-metric between propositional formulas are given,some basic properties such as union-intersection inference rules are discussed,three different approximate reasoning patterns are put forward in t logic metric space,and their equivalent relations are proved.Using the randomization method of valuation set,the concepts of t randomized truth degree,t randomized similarity degree and t randomized pseudo-metric between propositional formulas,t randomized divergent degree and t randomized consistent degree of theory ? are given,some basic theories such as t randomized divergent degree and consistent degree are studied,three different approximate reasoning patterns are proposed in t randomized logic metric space,and their equivalent relations are proved.Using induced function of propositional formula,the concepts of ?-t truth degree,?-t similarity degree and ?-t pseudo-metric between formulas relative to local finite theory ? are given,some basic operation properties such as MP and HS rules are proved.