PROBLEM ELIMINASI CUT PADA LOGIKA LBB’Ink

Abstract

In the present paper we study the problem of  the cut elimination in logics LBB’I_nk , i.e. logics obtained from LBB’I by adding a rule called (n®k) rule. It is known that  the cut elimination theorem for LBB’I and its standard extensions can be proved using some modifications of the method used by Gentzen in 1935 to prove the cut elimination theorem for Intuitionistic Logic. We extend the modifications to show that LBB’I_nk  enjoy the cut elimination theorem when k=1. On the  other side, we give a counter example sequent to show that the cut elimination theorem does not work for  LBB’I_nk  when k>1.