Abstract:

By means of theory of truth degrees of formulas, the properties of the generalized roots of theories in classical two-valued logic system, lukasiewicz propositional logic, Gdel propositional logic, and the R0-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.

Key words: propositional logic system, generalized roots, divergence degree, consistency degree, membership degree