Betweenness Relations and Binary Operators: An Algebraic and Logical Approach

Ivo Düntsch presents an algebraic treatment of the ternary betweenness relation familiar from geometry. The talk introduces betweenness algebras and the logic K^#, which uses two complementary binary modalities. Its algebraic models are Boolean algebras equipped with two binary modal operators linked by a connecting condition. This extends unary mixed logic and increases the expressive power of classical modal logic. The presentation develops properties of these structures from joint work with R. Gruszczyński and P. Menchón at Nicolaus Copernicus University.