Abstract
For the approximate reasoning method is extended to general probability space, we define three-valued logic (p,q,r) measure in discrete probability space and quasi-truth degree of formula in Lukasiewicz 3-valued logic system which is popularized from truth degree of formula. We also prove that the set of quasi-truth degree of all formulas in the range of [0,1] is dense and give the general expression of quasi-truth degree when (p,q,r)=(1/6,2/6,3/6) and (p,q,r)=(1/7,2/7,4/7). Finally, we define similarity degree between formulas and a kind of pseudo-distance in the set of all formulas, so provide a possible structure of approximate reasoning theory.
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