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. ***
