This paper is focused on the study of modal logics defined from valued Kripke frames, and particularly, on computability and expressibility questions of modal logics of transitive Kripke frames evaluated over certain residuated lattices. It is shown that a large family of those logics -- including the ones arising from the standard MV and Product algebras -- yields an undecidable consequence relation. Later on, the behaviour of transitive modal Lukasiewicz logic is compared with that of its non transitive counterpart, exhibiting some particulars concerning computability and equivalence with other logics. We conclude the article by showing the undecidability of the validity and the local SAT questions over transitive models when the Delta operation is added to the logic.

中文翻译：

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关于传递模态多值逻辑

本文重点研究由可值 Kripke 框架定义的模态逻辑，特别是在某些剩余格上评估的传递 Kripke 框架的模态逻辑的可计算性和可表达性问题。结果表明，这些逻辑的一大类——包括由标准 MV 和乘积代数产生的逻辑——产生了不可判定的结果关系。稍后，将传递模态 Lukasiewicz 逻辑的行为与其非传递对应物的行为进行比较，展示了与其他逻辑有关的可计算性和等价性的一些细节。我们通过在逻辑中添加 Delta 操作时展示有效性的不可判定性和传递模型的局部 SAT 问题来结束本文。