The Structure of Lattices of Subframe Logics
The Structure of Lattices of Subframe Logics
复制标题
子帧逻辑的格结构
DOI：
10.1016/s0168-0072(96)00049-8
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发表时间：
1997
期刊：
影响因子：
--
通讯作者：
F. Wolter
中科院分区：
文献类型：
--
作者：
F. Wolter
本文研究了正规单模子框架逻辑和多模子框架逻辑的格结构，即框架在某种类型的子结构下是闭合的那些模逻辑。几乎所有的基本模态逻辑都属于这一类。应用的主要格论工具是完整格的分裂的概念，它被证明与框架的“几何”和“拓扑”有关，与Klipke完备性和公理化问题有关。我们详细研究了包含K4的子框逻辑、包含多通道Altnand的子框逻辑以及属于时态逻辑的子框逻辑。
This paper investigates the structure of lattices of normal mono- and polymodal subframe logics, i.e., those modal logics whose frames are closed under a certain type of substructures. Nearly all basic modal logics belong to this class. The main lattice theoretic tool applied is the notion of a splitting of a complete lattice which turns out to be connected with the “geometry” and “topology” of frames, with Kripke completeness and with axiomatization problems. We investigate in detail subframe logics containing K4, those containing polymodal Altnand subframe logics which are tense logics.