Case Calculus for Classical Logic by Kensuke Baba

After the work of Gri n in 1990, there have been many works to extend the Curry-Howard isomorphism for classical logic. Most of these research uses sequent calculus with multiple conclusions. In this paper, we introduce a new natural deduction formulation with one conclusion for implicational classical logic. The idea of the formulation is based on proof by \case analysis". It is natural and captures our intuition in logical reasoning. We de ne reduction rules and prove weak normalization. As a corollary, we have the subformula property for normal proofs. The natural deduction systems proposed so far does not have subformula property. We also explain some computational meaning of our calculus by showing the simulation of -reduction, disjunction and catch/throw.