论文标题
足够的多种逻辑局部表格性条件
Sufficient conditions for local tabularity of a polymodal logic
论文作者
论文摘要
关于关系结构和多峰逻辑，我们描述了保留局部表格性的操作。这为模态逻辑的局部表格性提供了新的足够语义和公理条件。主要结果是以下。 我们表明，局部表格性不取决于反射性。也就是说，给定帧的类$ \ Mathcal {f} $，考虑框架$ \ Mathcal {f}^\ Mathrm {r} $的类，其中将反射闭合操作应用于$ \ Mathcal {f} $的每个帧中的每个帧中的每个关系。我们表明，如果$ \ mathcal {f}^\ mathrm {r} $的逻辑是本地表格的，则$ \ mathcal {f} $的逻辑也是本地表格的。 然后，我们考虑在kripke框架上的总和的操作，其中一个框架的家族被另一帧的元素索引。我们表明，如果索引的逻辑和汇总的逻辑都是局部表格的，则相应总和的逻辑也是局部表格的。 最后，使用以前的定理，我们描述了保留本地表格性的逻辑的操作：我们提供一组公式，使得两个规范局部表格逻辑与这些公式的融合扩展是本地表格的。
On relational structures and on polymodal logics, we describe operations which preserve local tabularity. This provides new sufficient semantic and axiomatic conditions for local tabularity of a modal logic. The main results are the following. We show that local tabularity does not depend on reflexivity. Namely, given a class $\mathcal{F}$ of frames, consider the class $\mathcal{F}^\mathrm{r}$ of frames, where the reflexive closure operation was applied to each relation in every frame in $\mathcal{F}$. We show that if the logic of $\mathcal{F}^\mathrm{r}$ is locally tabular, then the logic of $\mathcal{F}$ is locally tabular as well. Then we consider the operation of sum on Kripke frames, where a family of frames-summands is indexed by elements of another frame. We show that if both the logic of indices and the logic of summands are locally tabular, then the logic of corresponding sums is also locally tabular. Finally, using the previous theorem, we describe an operation on logics that preserves local tabularity: we provide a set of formulas such that the extension of the fusion of two canonical locally tabular logics with these formulas is locally tabular.
