Theory Of∑-([α,β]-Truth Degree)of Propositions In N-valued SMTL Logical System

At the beginning of this century, Professor Wang Guojun introduces the conceptof truth degrees of the proposition in two valued propositional logic based on theuniform probability, the theory of the quantitative logic is established and a model forapproximate reasoning is put forward therefore. After extensively researching, thequantitative logic has been developed into a relatively mature subject. The aim of thequantitative logic lies in introducing numerical computations into the mathematicallogic, making the mathematical logic have some flexibility and expanding the range ofits possible applications. Its basic starting point is to make the basic concepts to thelevel, and the concept of truth degree of propositions is the most basic which is putforward based on the tautologies are to be leveled. Similarity degree and pseudodistance and some other concepts are introduced on the basis of the truth degrees ofpropositions.In addition, in order to depict the propositions to be bad or good more detailed,concepts of∑(α tautology)and∑(β Contradiction)are put forward by professorWang and other scholars. The major objective of this article is to introduce the conceptof∑([α,β] truth degree)of propositions by grading the concepts of both∑(α tautology)and∑(β Contradiction) at the same time which can depicts notonly the degree of a proposition as a∑(α tautology)but also the degree of thisproposition as a∑(β Contradiction). The∑([α,β] truth degree) of a propositionreflects the degree that this proposition is neither good nor bad when α and βareclose to half. Based on the theory of∑([α,β] truth degree) of propositions, amodel for approximate reasoning under the unified frame of n-valued SMTL system isestablished.The article is divided into three chapters:areThe first chapter gives some prepared knowledge that the full text needs to use.The second chapter first puts forward the concept of∑(α truth degree) ofpropositions in n-valued SMTL logical system. Secondly, concepts of∑similaritydegree and∑pseudo distancebetween propositions are introduced and a possibleframe for approximate reasoning is given.The third chapter puts forward the concept of∑([α,β] truth degree) ofpropositions in n-valued SMTL logical system. The inference rules about MP and HSare given. In the end, the∑([α,β] similarity degree) between formulas is givenon the basis of∑([α,β] truth degree) and this make it possible to develop a kind of approximate reasoning based on the theory of∑([α,β] truth degree).