TEOREMA ELIMINASI CUT PADA SISTEM LOGIKA FLgc DAN FLw,gc

Abstract

It is well known that the cut elimination theorem does not hold for FLc dan FLw,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 (FLgc), which is equivalent to FLc. Similar result is also shown for system FL with both weakening and global contraction rule (FLw,gc), which is equivalent to FLw,c. In the present paper we modify and develop the method used to prove the cut elimination for proportional logic FLgc to show that the cut elimination theorem even holds for the predicate logics FLgc dan FLw,gc.