INTERPOLATION THEOREM FOR NONCOMMUTATIVE STANDARD EXTENSIONS OF LOGIC BB’I

Abstract

Maehara in [Maehara, 1960/1961] introduces a proof-theoretical method for proving the interpolation theorem for standard logics. In the present paper we modify Maehara’s method to prove the interpolation theorem for the systems LBB’IK, LBB’IW and LBB’IKW introduced in [Bayu Suraraso, 2005] and consequently the interpolation theorem holds for the logics BB’IK, BB’IW and BB’IKW.