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On the Complexity of Nonassociative Lambek Calculus with Unit

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Abstract

Nonassociative Lambek Calculus (NL) is a syntactic calculus of types introduced by Lambek [8]. The polynomial time decidability of NL was established by de Groote and Lamarche [4]. Buszkowski [3] showed that systems of NL with finitely many assumptions are decidable in polynomial time and generate context-free languages; actually the P-TIME complexity is established for the consequence relation of NL. Adapting the method of Buszkowski [3] we prove an analogous result for Nonassociative Lambek Calculus with unit (NL1). Moreover, we show that any Lambek grammar based on NL1 (with assumptions) can be transformed into an equivalent context-free grammar in polynomial time.

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  1. Faculty of Mathematics and Computer Science, University of Warmia and Mazury, Żołnierska 14, Olsztyn, Poland

    Maria Bulińska

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  1. Maria Bulińska
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Correspondence to Maria Bulińska.

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Bulińska, M. On the Complexity of Nonassociative Lambek Calculus with Unit. Stud Logica 93, 1–14 (2009). https://doi.org/10.1007/s11225-009-9205-2

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