Proof Normalisation in a Logic Identifying Isomorphic Propositions

Abstract

We define a fragment of propositional logic where isomorphic propositions, such as A ∧ B and B ∧ A, or A ⇒ (B ∧ C) and (A ⇒ B) ∧ (A ⇒ C) are identified. We define System I, a proof language for this logic, and prove its normalisation and consistency.