In 1961 Maehara introduced a proof-theoretical method to prove the interpolation theorem for standard logics. By developing Maehara’s method, we can prove interpolation theorem for some non-standard logics, including the commutative predicate  logics  Fle dan Fle,w. In the present paper we show that by modifying Maehara’s method we can also prove the interpolation theorem for non-commutative predicate logics FL and FLw.
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