CAJ | 학술논문

以经典命题逻辑中公式的向量表示形式为基础，利用三值?ukasiewicz逻辑系统中公式的赋值及赋值顺序给出了公式的向量表示形式。利用向量表示形式给出了公式真度的定义和公式间的相似度、伪距离的计算公式；得到了公式的真度和公式间相似度、伪距离的一些简单性质；证明了在伪距离空间(F(S)'ρ)中，一元运算逻辑连接词?和二元运算逻辑连接词?、ú、ù均关于ρ是连续的。相关结论为进一步研究多值?ukasiewicz逻辑系统中近似推理打下了夯实的基础。
이경전명제라집중공식적향량표시형식위기출，이용삼치?ukasiewicz라집계통중공식적부치급부치순서급출료공식적향량표시형식。이용향량표시형식급출료공식진도적정의화공식간적상사도、위거리적계산공식；득도료공식적진도화공식간상사도、위거리적일사간단성질；증명료재위거리공간(F(S)'ρ)중，일원운산라집련접사?화이원운산라집련접사?、ú、ù균관우ρ시련속적。상관결론위진일보연구다치?ukasiewicz라집계통중근사추리타하료항실적기출。
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?ukasiewicz propo-sitional 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 ? , ú , ù 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?ukasiewicz propositional logic system.