An almost general splitting theorem for modal logic
An almost general splitting theorem for modal logic
复制标题
模态逻辑的一个几乎通用的分裂定理
DOI：
10.1007/bf00370158
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发表时间：
1990
期刊：
影响因子：
0.7
通讯作者：
M. Kracht
中科院分区：
文献类型：
--
作者：
M. Kracht
给定一个正规（多）模态逻辑Θ，给出了其逻辑LA分裂Θ的正规扩张格的可表示代数A的一个特征.这是Rautenberg [10]和[11]的实质性推广，其中假设Θ是弱传递的，A是有限的。作为一个直接结果，我们还得到了Blok [2]的一个结果，即对于所有无圈的有限ALA，K的正规扩张格是分裂的。虽然我们坚信这是真的，但我们还不能证明，如果逻辑Λ分裂了Θ的扩张格，那么Λ是在Θ上可表示的代数的逻辑;在这方面，我们的结果仍然是部分的。
Given a normal (multi-)modal logic Θ a characterization is given of the finitely presentable algebras A whose logics LA split the lattice of normal extensions of Θ. This is a substantial generalization of Rautenberg [10] and [11] in which Θ is assumed to be weakly transitive and A to be finite. We also obtain as a direct consequence a result by Blok [2] that for all cycle-free and finite ALA splits the lattice of normal extensions of K. Although we firmly believe it to be true, we have not been able to prove that if a logic Λ splits the lattice of extensions of Θ then Λ is the logic of an algebra finitely presentable over Θ; in this respect our result remains partial.