9 May 2018, Algebra|Coalgebra Seminar, Nick Bezhanishvili

In recent years there has been a renewed interest in the modal logic community toward Boolean algebras equipped with binary relations. The study of such relations and their representation theory has a long history, and is related to the study of point-free geometry, point-free topology, and region based theory of space. Our primary examples of Boolean algebras with relations will be de Vries algebras, which are dual to compact Hausdorff spaces. Our main goal is to use the methods of modal logic and universal algebra to investigate the logical calculi of Boolean algebras with binary relations. This will lead, via de Vries duality, to simple propositional calculi for compact Hausdorff spaces, Stone spaces, etc.