Unified Theory of Truth Degrees in n-Valued S-MTL Propositional Logic

The concept of strong regular implication operator and the n-valued S-MTL propositional logic system are introduced.Based on probability measure the truth degree of formula is defined and its integral expression is given and the inference rules w.r.t the truth degrees is proved.Moreover,similarity degrees among formulas are proposed and a pseudo-metric is defined therefrom on the set of formulas.The continuity of logical operators w.r.t the pseudo-distance is proved,and hence a possible framework suitable for developing approximate reasoning theory in n-valued S-MTL propositional logic is established.