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

• Autorzy: Paweł Płaczek
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Substructural logic; Lambek calculus; nonassociative linear logic; sequent system; PTime complexity

• Wydawca: Wydawnictwo Uniwersytetu Łódzkiego
• Czasopismo: Bulletin of the Section of Logic
• Rocznik: 2021
• Tom: 50
• Numer: 1
• Strony: 55-80

Daty

wydano

2021-03-30

Twórcy

autor

Paweł Płaczek

• Adam Mickiewicz University, Faculty of Mathematics and Computer Science Uniwersytetu Poznanskiego 4, 61-614 Poznan, Poland

• https://orcid.org/0000-0002-8086-3150

Bibliografia

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Identyfikatory

DOI

10.18778/0138-0680.2020.25