Research On Truth Degree In Two Kinds Of Propositional Logic Systems

By combining absolute truth degree with T- truth degree, the concept of T- absolute truth degree is given and its properties are discussed in three- valued ?ukasiewicz propositional logic system. Also the T- absolute similarity degree and pseudo- distance between two formulas are defined by using the T- absolute truth degree. It is proved that logic operations are continuous.The truth degree of formulas is provided by the vector representations in three- valued ?ukasiewicz propositional logic system. On this base, the formulas to calculate the similarity degree and pseudo- metric are defined. Relevant conclusions are obtained.Based on the infinite product of unevenly distributed probability space, this paper introduces the probability truth degree in four- valued G?del propositional logic system. It is proved that the set of probability truth degree of all formulas has no isolated point in [0,1]. The conceptions of probability similarity degree and pseudo- metric between two formulas are defined. Moreover, the probability logic metric space is built. It is proved that this space has no isolated point.