A sequent is a pair (Γ, Δ), which is true under an assignment if either some formula in Γ is false, or some formula in Δ is true. In L₃-valued propositional logic, a multisequent is a triple Δ|Θ|Γ, which is true under an assignment if either some formula in Δ has truth-value t, or some formula in Θ has truth-value m, or some formula in Γ has truth-value f. Correspondingly there is a sound and complete Gentzen deduction system G for multisequents which is monotonic. Dually, a co-multisequent is a triple Δ: Θ: Γ, which is valid if there is an assignment v in which each formula in Δ has truth-value ≠ t, each formula in Θ has truth-value ≠ m, and each formula in Γ has truth-value ≠ f. Correspondingly there is a sound and complete Gentzen deduction system G⁻ for co-multisequents which is nonmonotonic.

序列是一对（Γ，Δ），如果Γ中的某些公式为假，或者Δ中的某些公式为真，则在赋值下为true。在L ₃值的命题逻辑中，乘数是一个三元Δ|Θ|Γ，在赋值下，如果Δ中的某些公式具有真值t，或者Θ中的某些公式具有真值m，或者在某个赋值下是真Γ中的公式具有真值f。相应地，存在针对单调的健全且完整的Gentzen演绎系统G。对偶是一个三重Δ：Θ：Γ，在有赋值v的情况下有效其中Δ中的每个公式的真值≠t，Θ中的每个公式的真值≠m，Γ中的每个公式的真值≠f。相应地有一个健全和完整的根岑演绎系统摹^-为共同multisequents是单调的。