TEOREMA ELIMINASI CUT PADA SISTEM LOGIKA FLgc DAN FLw,gc

Abstract

It is well known that the cut elimination theorem does not hold for FL_c dan FL_w,c, neither for propositional level nor predicate level. On the other hand, it has been proved that for the propositional level the cut elimination theorem holds for FL with global contraction (FL_gc), which is equivalent to FL_c. Similar result is also shown for system FL with both weakening and global contraction rule (FL_w,gc), which is equivalent to FL_w,c. In the present paper we modify and develop the method used to prove the cut elimination for proportional logic FL_gc to show that the cut elimination theorem even holds for the predicate logics FL_gc dan FL_w,gc.