Abstract:

Based on conditional probability, using the randomization method of valuation set, the concept of D-conditional truth degree of formulas is introduced in the 3valued Gdel propositional logic system. The MP rule and HS rule of D-conditional truth degrees are proved. The concepts of D-conditional similarity and Dconditional pseudodistances between formulas are introduced and D-conditional logic metric space is built. Several properties of D-conditional pseudodistances are deduced and it is proved that the D-conditional pseudo-distances is continuous on the logical operation of “∨”, “∧”, “→” in D-conditional logic metric spaces. Three different types of approximate reasoning patterns are discussed in D-conditional logic metric space, and the relationships between them are studied.

Key words: logic system G₃; D-conditional truth degree; D-conditional pseudo-distances; D-conditional logic metric space; approximate reasoning