论文标题
有限价值的模态逻辑中的框架可确定性
Frame definability in finitely-valued modal logics
论文作者
论文摘要
在本文中，我们研究了有限评价的模态逻辑中的框架可确定性，并通过合适的翻译建立了两个主要结果：（1）在有限评估的模态逻辑中，一个人不能定义比在经典模态逻辑中可以定义的框架多的类别（cf.经典的模态逻辑（包括基于有限的Heyting和\ MV-Algebras，甚至\ bl-algebras的模态逻辑）。例如，这样一个人们可以观察到著名的戈德布拉特 - 托马森定理立即适用于这些逻辑。特别是，我们从〜\ citep {te}获得了中心结果，并以更简单的证明并回答该论文中留下的一个开放问题之一。此外，提出的翻译使我们能够确定一大类有限评估的模态逻辑的计算复杂性。
In this paper we study frame definability in finitely-valued modal logics and establish two main results via suitable translations: (1) in finitely-valued modal logics one cannot define more classes of frames than are already definable in classical modal logic (cf.~\citep[Thm.~8]{tho}), and (2) a large family of finitely-valued modal logics define exactly the same classes of frames as classical modal logic (including modal logics based on finite Heyting and \MV-algebras, or even \BL-algebras). In this way one may observe, for example, that the celebrated Goldblatt--Thomason theorem applies immediately to these logics. In particular, we obtain the central result from~\citep{te} with a much simpler proof and answer one of the open questions left in that paper. Moreover, the proposed translations allow us to determine the computational complexity of a big class of finitely-valued modal logics.
