Reasonable Solution For Generalizad MP Problems In Propositional Logic And New Reverse Triple I Method

As is known to all, the characteristics of mathematical logic lies in formalization and symbolization. Mathematical Logic and Computational Mathematics have very different style. The former emphasizes formal inference, but the latter pays more attention to numeric calculation. The former emphasizes strict argument, but the latter allows approximate analysis. While the logical reasoning methods have been widely used in many fields such as the automatic proof of theorems, reasoning about knowledge and logical program design, the numerical calculation seems to be a method that looks so different form the formal inference. Because human brain and inference methods have uncertainty which lead inference to be approximate, the introduction of numerical calculation for the mathematical logic systems which can make it have some flexibility is very necessary. To the mathematical logic systems, this flexibility also enlarges its possible range of applications. For this purpose, Professor Wang has established Quantitative Logic theory. In this theory, Professor Wang proposed the concept of truth degrees of formulas which can describe the degree of a formula's reliability, and then he further put forward two concepts: Similarity degree between two formulas and pseudo-distance. Based on these, both divergency degree and consistency degree of theories were proposed, Professor Wang successfully creative a complete kind of approximate reasoning mechanism and points out the way of distinguish different consistence degrees of theories.In order to take fuzzy reasoning into logical framework and lay the strict logical foundation for it from syntactic and semantic , this thesis not only transformed the problem from FMP into GMP by the transplantation of fuzzy reasoning's formalization which occurred in the classical propositional logic systems, but also proved reasonable solutions'existence of a new GMP solving mechanism which introduced by sustentation degree that comes from truth degree of proposition in propositional logic. This is one of the problems studied in this paper.Soon afterwards, Professor Wang proposed the principle that if the supportation degree from premise to conclusion excesses 0.5, then they are advisable as for fuzzy reasoning. This principle is known as"principle of credit beyond half". Using this principle, Wang established a new Triple-I method for solving FMP problems. This work set an initial way of bringing the fuzzy reasoning method into artificial intelligence. As a purpose for designing fuzzy reasoning system, Song Shiji generalized Triple-I method into reversed Triple-I method. Based Wang's half advisability principle, this paper proposed a new reversed Triple-I method for solving FMP problems.The main work of this paper includes:1. By means of truth degrees of formulas, this paper puts forward a new concept of sustentation degree among formulas in classical propositional logic. Reasonable solution based on the idea of sustentation degree for problems of generalized modus ponens is introduced, and the existence theorem of reasonable solutions is proved.2. It is proved that R0 -triangular norm satisfies the Wang's principle of credit beyond half. The corresponding new triple I method based on R₀ implication operator of fuzzy reasoning is given.