王译恒 | From weakly topological quasi-Boolean algebra to weak pre-rough algebra and closely related structures: an algebraic and logical investigation

我所23级博士研究生王译恒、厦门大学林哲副教授与印度Jadavpur大学Mihir Chakraborty教授合作的论文From weakly topological quasi-Boolean algebra to weak pre-rough algebra and closely related structures: an algebraic and logical investigation发表于国际期刊Logic Journal of the IGPL第34卷第3期。Logic Journal of the IGPL是一本由牛津大学出版社出版的逻辑类国际期刊，主要聚焦于理论逻辑和应用逻辑的各类领域。该期刊收录于SCIE，长期位列JCR排名Q2。

作者：王译恒、林哲、Mihir Chakraborty
原文链接 https://doi.org/10.1093/jigpal/jzag009

论文摘要

Over the past few years, a new cluster of abstract algebras has emerged within the general context of research in rough set theory. Among them, one is the weakly topological quasi-Boolean algebra. This paper studies the vicinity of weakly topological quasi-Boolean algebra from algebraic and logical perspectives. The weak pre-rough algebra is defined, and a cluster of intermediate algebras between it and the quasi-Boolean algebra is explored. The interrelationship and independence among them are presented. We also establish sound and complete sequential systems for these algebras. Further, we show the finite model property and construct decidable algorithms for weakly topological quasi-Boolean algebra and its weaker variants by context-free grammars. Rough set models of some of these algebras have been presented.

成果介绍

该论文研究了一系列坐落于弱拓扑拟布尔代数和弱粗糙代数之间的结构，从代数和逻辑的角度出发对这些结构进行了系统研究，得到了有穷模型性、判定性和判定算法等良好结果。由于这些结构在粗糙集理论中具有特别的意义，该论文还从粗糙集理论的角度出发对这些结构进行了讨论。