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One-Sided Sequent Systems for Nonassociative Bilinear Logic: Cut Elimination and Complexity

100%

Płaczek P.

Bulletin of the Section of Logic

2021

tom 50

nr 1

55-80

Bilinear Logic of Lambek amounts to Noncommutative MALL of Abrusci. Lambek proves the cut–elimination theorem for a one-sided (in fact, left-sided) sequent system for this logic. Here we prove an analogous result for the nonassociative version of this logic. Like Lambek, we consider a left-sided system, but the result also holds for its right-sided version, by a natural symmetry. The treatment of nonassociative sequent systems involves some subtleties, not appearing in associative logics. We also prove the PTime complexity of the multiplicative fragment of NBL.

Ograniczanie wyników

1 Bulletin of the Section of Logic

1 Płaczek P.

1 2021

Wyniki wyszukiwania

One-Sided Sequent Systems for Nonassociative Bilinear Logic: Cut Elimination and Complexity