Probability-Truth Logic
Keywords:
Membership function, Measure, Conditional distribution, Bi-conditional distribution, Elementary event, Bayes rule.Abstract
In this paper, a new kind of infinite logic will be introduced. The elements of this logic are truth function that assigns truth value belongs to the range [0,1] to any statement representing degree of truth and probability function that assigns a value ranging [0,1] to any random event representing degree of likelihood (both truth and probability are measures satisfying the classical axioms of probability theory). New axioms and definitions will be added to the axioms and definitions of probability theory to represent intersection, union, implication and double implication between truth statements, probabilistic events and truth statements and probabilistic events. By this, we can evaluate degree of truth and degree of likelihood and the interaction between them.
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