Properties and applications of the roots of theories in propositional logic systems
Jianchen Zhang · Journal of Shandong University · 2013
By means of theory of truth degrees of formulas,the properties of the generalized roots of theories in classical two-valued logic system,ukasiewicz propositional logic,G del propositional logic,and the R 0-propositional logic were first studied according to deduction theorems.Then,it was proved that all consequences of a theory Γ,named D(Γ),were completely determined by its generalized root whenever Γ had a generalized root.Finally,a new algorithm of divergence degree,consistency degree,and Membership degree of Γ-conclusion was obtained.