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The logic of bunched implication BI provides a framework for reasoning aboutresource composition and forms the basis for an assertion language ofseparation logic which is used to reason about software programs. PropositionalBI is obtained by freely combining propositional intuitionistic logic andmultiplicative intuitionistic linear logic. It possesses an elegant prooftheory: its bunched calculus combines the sequent calculi for these logics.Several natural extensions of BI have been shown as undecidable, e.g. BooleanBI which replaces intuitionistic logic with classical logic. This makes thedecidability of BI, proved recently via an intricate semantical argument,particularly noteworthy. However, a syntactic proof of decidability has thusfar proved elusive. We obtain such a proof here using a proof-theoreticargument. The proof is technically interesting, accessible as it uses the usualbunched calculus (it does not require any knowledge of the semantics of BI),yields an implementable decision procedure and implies an upper bound on thecomplexity of the logic.

A syntactic proof of decidability for the logic of bunched implication BI