Proof theory of the calculus of relations

Abstract

The calculus of relations is a rich discipline that spanned much of the history of symbolic logic, with contributions ranging from De Morgan to Tarski. Yet not much is known about the proof theory for the calculus of relations. For example, a sequent calculus developed by Maddux has the shortcoming of not being cut-free. In this work we will develop a sequent calculus that is cut-free. To do this we will use a procedure developed by Negri & von Plato to transform geometric theories into rules for a sequent calculus.