A cut-free proof theory for boolean BI (via display logic)

Abstract

We give a display calculus proof system for Boolean BI (BBI) based on Belnap’s general display logic. We show that cut-elimination holds in our system and that it is sound and complete with respect to the usual notion of validity for BBI. We then show how to constrain proof search in the system (without loss of generality) by means of a series of proof transformations. By doing so, we gain some insight into the problem of decidability for BBI.