Mathematical Sciences: Self-Dual Stone Algebras and Applications

小行星9409741 这个职业发展奖支持分析自对偶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，是由概率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，人们就会重新审视原来的应用，并寻找新的应用。 的观点是一个分类的，通过广泛的工作，使用同调方法在代数。 这项工作借鉴了逻辑和模型理论，一般拓扑，非标准分析和偏序集的不同领域-以及格理论，它仍然是计算机科学，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. ***