The theory of Γ-truth degrees of formulas and limit theorem in Lukasiewicz propositional logic

The theory of truth degrees of formulas and limit theorem in Lukasiewicz n-valued propositional logic has been investigated again.(1) In Lukasiewicz n-valued propositional logic, a form of truth degree's definition described by valuations is given which indicates directly from the aspects of valuations that the truth degree of a formula is membership degree for the formula belonging to tautologies;(2) In Lukasiewicz n-valued propositional logic, a concept ofΓ-truth degree of a formula relative to locally finite theory Γ is proposed through the valuation's form of truth degree, some equivalent forms with properties of Γ-truth degrees are given;(3) The limit theorem about Γ-truth degree in Lukasiewicz nvalued propositional logic is proved;(4) A reasonable form of Γ-truth degree in Lukasiewicz continuity-valued propositional logic and a symmetrical theorem of truth degree in Lukasiewicz propositional logic are given;(5) In Lukasiewicz n-valued propositional logic, the problem of Γ-truth degrees of formulas relative to infinite theory is discussed by limit method and the valuation's form of Γ-truth degrees.