Equivalence of multiplicative fragments of cyclic linear logic and noncommutative linear logic
In this paper we consider two associative noncommutative analogs of Girard's linear logic. These are Abrusci's noncommutative linear logic and Yetter's cyclic linear logic.
We give a linear-length translation from the multiplicative fragment of Abrusci's noncommutative linear logic into the multiplicative fragment of Yetter's cyclic linear logic and vice versa. As a corollary we obtain that the decidability problems for derivability in these two calculi are in polynomial time reducible to each other.
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