An Equivalent Definition and Some Properties of Truth Degrees in ALukasiewicz Proposition Logic System

The theory of truth degrees in the Lukasiewicz proposition logic system is investigated in this paper.Firstly,an intuitionistic equivalent form of the definition of truth degrees in the Lukasiewicz n-valued proposition logic system is given;Secondly,the proofs of the limit theorem that connect the theory of truth degrees of Lukasiewicz n-valued proposition logic system and Lukasiewicz continuity-valued is simplified through the equivalent form of definition;Thirdly,it is proved that the truth degree of a formula keeps invariability when an exchange takes place among its atomic formula and the negation;Fourthly,the relationship between inference rules and truth degrees is discussed.A precise equation about MP rule and truth degrees is obtained,and the consequence about the union inference rule of truth degrees is also obtained in Lukasiewicz proposition logic system.