In this paper, we investigate the many-valued version of coalgebraic modal logic through predicate lifting approach. Coalgebras, understood as generic transition systems, can serve as semantic structures for various kinds of modal logics. A well-known result in coalgebraic modal logic is that its completeness can be determined at the one-step level. We generalize the result to the finitely many-valued case by using the canonical model construction method. We prove the result for coalgebraic modal logics based on three different many-valued algebraic structures, including the finitely-valued {\L}ukasiewicz algebra, the commutative integral Full-Lambek algebra (FL$_{ew}$-algebra) expanded with canonical constants and Baaz Delta, and the FL$_{ew}$-algebra expanded with valuation operations.

翻译：在本文中,我们通过上游升起方法调查了多种有价值的煤眼模型逻辑。煤眼可被理解为通用过渡系统,可以用作各种模式逻辑的语义结构。煤眼模式逻辑的一个众所周知的结果是,其完整性可以在一步骤一级确定。我们通过使用金字塔模型建设方法,将结果概括为有一定价值的多值案例。我们证明了基于三种不同有价值的代数结构的煤眼模型逻辑的结果,包括有一定价值的苏卡西韦茨代数结构、与运河常数和巴兹三角洲相扩大的通性整体全成Lambek代数(FL$+ ⁇ w}$-algebra),以及与估值业务扩大的FL$+ ⁇ w}$-algebra。