Mathematical Sciences: Self-Dual Stone Algebras and Applications

9409741 Gehrke这个职业进阶奖支持分析自对偶斯通代数结构的数学研究。格中的自对偶性，特别是在Stone代数中的重要性，是由在概率和粗糙集代数中的条件事件结构中的应用所激发的。一旦对自我二元性有了更好的理解，原始的申请将被重新审查，并寻求新的申请。这个观点是一个范畴的观点，是通过代数中同调方法的广泛工作而发展起来的。这项工作借鉴了逻辑和模型理论、一般拓扑、非标准分析和部分有序集的各个领域，以及晶格理论，它仍然是计算机科学、人工智能和专家系统中逻辑研究的主要工具之一。＊＊＊

9409741 Gehrke This career advancement award supports mathematical research analyzing the structure of self-dual Stone algebras. The importance of self-duality in lattices, and particularly in Stone algebras, was motivated by applications to conditional event structures in probability and rough set algebras. Once a better understanding of the self-duality is accomplished, the original applications will be reexamined and new ones sought. The point of view is a categorical one, developed through extensive work using homological methods in algebra. The work draws on diverse fields of logic and model theory, general topology, nonstandard analysis and partially ordered sets - as well as lattice theory, which still remains one of the main tools in the study of logics for computer science, artificial intelligence and expert systems. ***