On the complexity of nonassociative Lambek calculus with unit

Studia Logica 93 (1):1 - 14 (2009)
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.
Keywords Nonassociative Lambek calculus  P-TIME decidability  Context-free grammar
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References found in this work BETA
Joachim Lambek (1968). The Mathematics of Sentence Structure. Journal of Symbolic Logic 33 (4):627-628.
Gerhard Jäger (2004). Residuation, Structural Rules and Context Freeness. Journal of Logic, Language and Information 13 (1):47-59.

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