Abstract
By means of infinite product of uniformly distributed probability spaces of cardinal n the concept of truth degrees of propositions in the n-valued generalized Lukasiewicz propositional logic system L * n is introduced in the present paper. It is proved that the set consisting of truth degrees of all formulas is dense in [0,1], and a general expression of truth degrees of formulas as well as a deduction rule of truth degrees is then obtained. Moreover, similarity degrees among formulas are proposed and a pseudo-metric is defined therefrom on the set of formulas, and hence a possible framework suitable for developing approximate reasoning theory in n-valued generalized Lukasiewicz proposi-tional logic is established.
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