Formula Of Degree Of Promotion And The L ~ * System Generation True Value Function Of Single Atom

It is well known that mathematical logic is characterized by its formalization and symbolization. Whether it is two-valued logic or multi-valued logic, it focus on forms of reasoning, and is less concerned about the numerical calculation. In2001, Professor Wang introducd the concept of truth degrees of formulas based on the idea of even probability in the classical two-valued propositional logic, making mathematical logic have the numerical calculation and some flexibility to expand its scope of application. In this paper, based on the concept of truth degrees of formulas, we mainly have done the folloeing three aspects of work. Firstly, based on the concept of truth degrees of formulas in Lukasiewicz3-valued logic, we introduce formulas of truth degree, applying the important mathematical idea of equations to the reseach of Lukasiewicz3-valued logic system. Secondly, concerning that the original concept of truth degrees is built on even probability, we use the more general non-even probability to define the concept of truth degrees of formulas, thereby expanding the practicality of the truth degree. Thirdly, we study features of truth value functions in the logic system L*. By the study of truth value functions, we can grasp better the concept of truth degrees and types of logical formulas.In Chapter2, based on the concept of truth degrees in Lukasiewicz three-valued propositional logic, we put forward the notion of logical equations and give an existence theorem on solutions of logical equations. We explore certain types of logic equations and give a fomula for the number of equivalence classes of their solution. It is proved that the conjunction of all solutions of a certain type of logic equations is a contradiction.In Chapter3, using3-valued non-even probability, we define a general concept of truth degrees of formulas in Lukasiewicz three-valued logic L3and Godel three-valued logic, respectively. We give constructive properties of the set of all truth values of formulas generated by a single atom in Lukasiewicz three-valued logic L3and Godel three-valued logic. We also give constructive properties of the set of all truth values of formulas generated by two atoms in Lukasiewicz three-valued logic L3In Chapter4, we discussed characterization of truth value functions induced by{(?),â†'}-type formulas generated by single atom in L*system. Six special formulas of{(?),â†'}-type and their truth value functions generated by single atom are given. It is proved that the number of truth value functions of single atom formulas is48and that the functions can simply obtained by the six special functions and the identify function via operations of (?) andâ†'. As a consequence, every formulae generated by single atom in L*systemis is provably equivalent to a formulae of {(?),â†'}-type.