A Note on Kanger’s Work on Efficient Proof Procedures

Abstract

Three of Stig Kanger’s works belong to proof theory taken in a wide sense: the monograph Provability in Logic of 1957, the paper “A simplified proof method for elementary logic” of 1963, and, in between these two, the mimeographed Handbok i logik written in 1959. I concur in Göran Sundholm’s remark in his paper of the present volume that Kanger’s main interest in this connection was not proofs themselves but provability and derivability and in particular the relation of these notions to semantical ones. A case in point is Kanger’s variant of Gentzen’s calculus of sequents for classical logic, LK, which Kanger develops in Provability in Logic. The purpose is there to give a new demonstration of Gödel’s completeness result that every valid formula is provable, i.e. has some proof, no matter which.