Completeness results for many-valued \Lukasiewicz modal systems and relational semantics
Completeness results for many-valued \Lukasiewicz modal systems and relational semantics
复制标题
多值 Lukasiewicz 模态系统和关系语义的完整性结果
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
B. Teheux
中科院分区：
文献类型：
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作者：
G. Hansoul;B. Teheux
本文研究了在Lukasiewicz多值逻辑中增加模态的问题，目的是得到Kripke语义的完备性结果.定义了一类模态多值逻辑及其相应的Kripke模型和模态多值代数。完整性的结果被认为是通过一个典型的模型的建设。完备性得到模态有限值逻辑，但也为模态多值系统与无穷演绎规则。我们引入了两类框架的有限值逻辑，并表明他们定义了两个不同的类Kripke完全逻辑。
The paper is dedicated to the problem of adding a modality to the \Lukasiewicz many-valued logics in the purpose of obtaining completeness results for Kripke semantics. We define a class of modal many-valued logics and their corresponding Kripke models and modal many-valued algebras. Completeness results are considered through the construction of a canonical model. Completeness is obtained for modal finitely-valued logics but also for a modal many-valued system with an infinitary deduction rule. We introduce two classes of frames for the finitely-valued logics and show that they define two distinct classes of Kripke-complete logics.