International Journal of Computational Intelligence Systems (Sep 2015)
The validity degree vectors of formulae in two-valued predicate logic
Abstract
By means of infinite product of uniformly distributed probability spaces of cardinal , the concept of -validity degrees and validity degree vectors of formulae in two-valued predicate logic are introduced. It is proved that the validity degree vectors of formulae can preserve the logical relation between formulae. Moreover, a consistency theorem is obtained which says that the -validity degree () of the quantifierfree first-order formula without any repeated predicate symbols or terms is independent of the natural number , and is a constant equal to the validity degree () of the corresponding proposition 0 in classical propositional logic.
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