Single-succedent System Approach to Boolean BI

It is known that the logic BI of bunched implications is useful for describing shared mutable data structures and resource-aware reasoning. It has recently been clarified that some classical versions of BI are especially useful for describing shared mutable data structures. In this paper, a single-succedent Gentzen-type sequent calculus GcBI for a classical version (called Boolean BI) of an intuitionistic BI is introduced. Some theorems for embedding GcBI into its intuitionistic version GiBI, which are analogous to the Glivenko and Gödel-Gentzen embedding theorems of classical logic into intuitionistic logic, are proved.