关键词: 三值Lukasiewicz逻辑系统, 真度, 相似度, 伪距离

Abstract: Based on vector representation of formula of classical propositional logic system, this paper gives a vector representation of formula by using assignment and assignment order of formula in three-valued Lukasiewicz propositional logic system. Firstly, this paper defines the truth degree of formula and gives the formula to calculate the similarity degree, pseudo-metric among formulas. Secondly, this paper obtains some simple properties of truth degree and similarity degree pseudo-metric among formulas. Thirdly, this paper proves that unary logical connection, binary operation logical connections→,∨,∧are continuous in pseudo-metric space (F(S),ρ). The related conclusions of this paper lay a solid foundation for further research of multi-valued Lukasiewicz propositional logic system.

Key words: three-valued Lukasiewicz propositional logic system, truth degree, similarity degree, pseudo-metric