On Truth Degree Theory In Axiomatic Extension System Of Goguen Propositional Logic

Axiomatic extension of n-valued Goguen propositional logic system is given by adding new connectors?and ?,which is denoted as ??,?.The definition of k truth degree,k similarity degree and k pseudo-metric between formulas are given in this system.Some properties such as MP rule and HS rule of k truth degree are proved.It is introduced that the k truth degree of formula keeps invariability when an exchange takes place between its atomic formulas and its negation.Subsequently,the calculation formula of k randomized truth degree,k randomized similarity degree and k randomized pseudo-metric between formulas are put forward in ??,?.Some basic properties such as MP rule and HS rule of k randomized truth degree are demonstrated.Meanwhile,three different types of approximate reasoning patterns are introduced,and they are proved to be equivalent.Then,with induced function,the concepts of ?-k truth degree,?-k similarity degree and ?-k pseudo-metric between formulas in ??,? relative to local finite theory ? under the k conjunction are given.Some basic theories such as intersection-union rule,MP rule and HS rule of ?-k truth degree are obtained.Last,using the randomization method of valuation sets,the ?-k randomized truth degree,?-k randomized similarity degree and ?-k randomized pseudo-metric in??,? relative to local finite theory ? under the k conjunction are put foward.Furthermore,the concepts of relative randomized divergence degree and the relative randomized consistency degree of theory r relative to the fixed theory ?0 in ??,?are introduced.The relationships between relative randomized divergence degree and relative randomized consistency degree are also established.