Tags:Bunched Implications Logic, Proof systems and Proof translations

Abstract:

In order to study proof translations in BI logic, we consider first the bunched sequent calculus LBI and then define a new labelled sequent calculus, called GBI. Therefore we propose a procedure that translates LBI proofs into GBI proofs and prove its soundness. Moreover we discuss some steps towards the reverse translation of GBI proofs into LBI proofs and propose an algorithm that is illustrated by some examples. Further work will be devoted to its proof of correctness and also to the design of translations of LBI proofs to TBI (labelled-tableaux) proofs.