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For the four-element Boolean algebra B 2 2 , a multisequent Г|Δ| ∑|∏ is a generalization of sequent Г →Δ in traditional B 2 2 valued first-order logic. By defining the truth-values of quantified formulas, a Gentzen deduction system G 2 2  for B 2 2 -valued first-order logic will be built and its soundness and completeness theorems will be proved.

Multisequent Gentzen Deduction Systems For B<sub>2</sub> <sup>2</sup>-Valued First-Order Logic