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.

Keywords

• two-valued predicate logic
• -validity degree
• validity degree vector
• consistency theorem