Multisequent Gentzen Deduction Systems For B2 2-Valued First-Order Logic

Abstract

For the four-element Boolean algebra B22, a multisequent Г|Δ|∑|∏ is a generalization of sequent Г→Δ in traditional B22 valued first-order logic. By defining the truth-values of quantified formulas, a Gentzen deduction system G22 for B22-valued first-order logic will be built and its soundness and completeness theorems will be proved.