Proof Transformations and Structural Invariance

In this paper we define the concept of a profile, which is a characteristic clause set, corresponding to an LK-proof in first-order logic, which is invariant under rule permutations. It is shown (via cutelimination) that the profile is even invariant under a large class of proof transformations (called “simple transformations”), which includes transformations to negation normal form. As proofs having the same profile show the same behavior w.r.t. cut-elimination (which can be formally defined via the method CERES), proofs obtained by simple transformations can be considered as equal in this sense. A comparison with related results based on proof nets is given: in particular it is shown that proofs having the same profile define a larger equivalence class than those having the same proof net.