The paper explores categorical interconnections between lattice-valued relational systems and algebras of Fitting’s lattice-valued modal logic. We define lattice-valued Boolean systems, and then we study adjointness and co-adjointness of functors defined on them. As a result, we get a duality for algebras of lattice-valued logic. Following this duality result, we establish a duality for algebras of lattice-valued modal logic.

中文翻译：

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Fitting格值逻辑和格值模态逻辑代数的范畴研究

本文探讨了格值关系系统和 Fitting 格值模态逻辑代数之间的分类互连。我们定义格值布尔系统，然后我们研究定义在它们上的函子的伴随性和共伴随性。结果，我们得到格值逻辑代数的对偶性。根据这个对偶性结果，我们为格值模态逻辑的代数建立了对偶性。