Mathematical Sciences: Self-Dual Stone Algebras and Applications

9409741格尔克职业进步奖支持分析自对偶Stone代数结构的数学研究。自对偶在格中的重要性，特别是在Stone代数中的重要性，是由概率代数和粗糙集代数中的条件事件结构的应用所激发的。一旦对自我二元性有了更好的理解，最初的申请将被重新审查，并寻求新的申请。这个观点是一种范畴观点，是通过使用代数中的同调方法进行广泛研究而发展起来的。这项工作涉及到逻辑和模型理论、一般拓扑学、非标准分析和偏序集等不同领域，以及格论，格论仍然是计算机科学、人工智能和专家系统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. ***