The validity degree vectors of formulae in two-valued predicate logic

Abstract

By means of infinite product of uniformly distributed probability spaces of cardinal n, the concept of n-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 n-validity degree τ_n(A) of the quantifierfree first-order formula A without any repeated predicate symbols or terms is independent of the natural number n, and is a constant equal to the validity degree τ (A⁰) of the corresponding proposition A0 in classical propositional logic.

Keywords:

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