CONNECTIONS BETWEEN CUTS AND MAXIMUM SEGMENTS

Abstract. Pairs of systems, which consist of a system of sequents and a natural deduction system for some parts of intuitionistic logic, will be considered. For some of these pairs of systems the well-known property that cut-free sequent derivations correspond to normal derivations in natural deduction will be improved. In derivations of the systems of sequents a special kind of cuts, maximum cuts, will be defined. It will be shown that sequent derivations with cuts which are not maximum cuts correspond to normal derivations in natural deduction. 2010 Mathematics Subject Classification: 03F05

Maximum Segments and Cuts

In the papers [1, 2, 4–6, 8] the similarities and differences between systems of sequents and systems of natural deduction for some fragments of intuitionistic logic were presented. The main goal of almost all of these papers was to study the connection between cut-free derivations and normal derivations