Integral Similarity Degree In S-Logic System And Distribution Of The Symmetrical Logic Formulas In L₄^*-Logic Metric Space

It is different from the usual similarity degree is defined based on truth degree, this paper put forward the integral similarity degree by use of S -implication operator in S -logic system, gave the inference properties of the integral similarity degree, established the pseudo-metric corresponding to the integral similarity degree. The continuity of the logical implication operator"-,∧,∨,â†'" in pseudo-metric space(FS(S), p) is proved, and the approximate reasoning in S -logic system is studied.In L4*-logic metric space, the concept of symmetric four value R0 function and symmetric logic formula are given. The counting problem of the symmetric logic formulas in the L4*-logic metric space is studied by solving the number of integer solutions of equation. It is realized that the integer solutions of equation by using MATLAB, thus the counting problem of the symmetric logic formulas in the L4*-logic metric space is solved. The counting formulas of the symmetric logic formulas with 3n,3n+1,3n+2 atoms in L4*-logic metric space are proved. By specific examples, the dissertation gave two methods realized the counting problem of the symmetrical logic formulas in L4*-logic metric space. It is concluded that the results are the same, and the conclusions are proved to be correct. It is obtained that the ratio of the number of symmetric formulas with n atoms over the numbers of all formulas with n atoms converges to zero when n tends to infinite. It is proved that the set of truth degree of symmetric logic formula is dense in [0,1].