On Classical Nonassociative Lambek Calculus
نویسنده
چکیده
CNL, intoduced by de Groote and Lamarche [11], is a conservative extension of Nonassociative Lambek Calculus (NL) by a De Morgan negation ∼, satisfying A∼/B ⇔ A\B∼. [11] provides a fine theory of proof nets for CNL and shows cut elimination and polynomial decidability. Here the purely proof-theoretic approach of [11] is enriched with algebras and phase spaces for CNL. We prove that CNL is a strongly conservative extension of NL, CNL has the strong finite model property, the grammars based on CNL (also with assumptions) generate the context-free languages, and the finitary consequence relation for CNL is decidable in polynomial time.
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