On normalizing disjunctive intermediate logics

Jonathan P. Seldin

pp. 237-248

in: Francine F. Abeles, Mark E. Fuller (eds), Modern logic 1850-1950, East and West, Basel, Birkhäuser, 2016

Abstract

In this paper it is shown that every intermediate logic obtained from intuitionistic logic by adding a disjunction can be normalized. However, the normalization procedure is not as complete as that for intuitionistic and minimal logic because some results which usually follow from normalization fail, including the separation property and the subformula property. However, in a few special cases, we can extend the normalization process to obtain new consistency proofs.