## Probability Truth Degrees of Formulas in MTL-Algebras Semantics

**ZUO Wei-bing;College of Mathematics and Information Science,North China University of Water Resources and Electric Power;**

Based on L-evaluation theory and by defining probability measure in MTL-algebra evaluation lattice and set of all formulas respectively,the concept of probability truth degree of formulas in MTL-algebras semantics is introduced by the integral method. The MP rule,HS rule and meet inference rules of probability truth degree are proved. At the meantime,the concept of probability similarity degree and pseudo-distances between formulas are introduced and the probability logic metric space is built. The theory of quantitative logic is expanded to lattice-valued logic based on MTL-algebra semantics,which makes it possible in graded reasoning in lattice-valued logic.

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