Towards an algorithmic construction of cut-elimination procedures

We investigate cut-elimination in propositional substructural logics. The problem is to decide whether a given calculus admits (reductive) cut-elimination. We show that, for commutative single-conclusion sequent calculi containing generalized knotted structural rules and arbitrary logical rules, the problem can be decided by resolution-based methods. A general cut-elimination proof for these calculi is also provided.