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Reports on Mathematical Logic

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No. 30

BAYU SURARSO and Hiroakira ONO

CUT ELIMINATION IN NONCOMMUTATIVE SUBSTRUCTURAL LOGICS
A b s t r a c t.
The present paper is concerned with the cut eliminability for some
sequent systems of noncommutative substructural
logics, i.e. substructural logics without exchange rule.
Sequent systems of several extensions of noncommutative logics **FL** and
**LBB'I**, which is sometimes called $\tw$,
will be introduced. Then, the cut elimination theorem and the
decision problem for them will be discussed in comparison with
their commutative extensions.

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