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Involutive Nonassociative Lambek Calculus: Sequent Systems and Complexity

100%

Buszkowski W.

Bulletin of the Section of Logic

2017

tom 46

nr 1/2

In [5] we study Nonassociative Lambek Calculus (NL) augmented with De Morgan negation, satisfying the double negation and contraposition laws. This logic, introduced by de Grooté and Lamarche [10], is called Classical Non-Associative Lambek Calculus (CNL). Here we study a weaker logic InNL, i.e. NL with two involutive negations. We present a one-sided sequent system for InNL, admitting cut elimination. We also prove that InNL is PTIME.

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

2 Bulletin of the Section of Logic

1 Buszkowski W.

1 Płaczek P.

1 2021

1 2017

Wyniki wyszukiwania

Involutive Nonassociative Lambek Calculus: Sequent Systems and Complexity

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