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[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.<\/jats:p>","DOI":"10.1007\/978-3-662-53826-5_5","type":"book-chapter","created":{"date-parts":[[2016,11,9]],"date-time":"2016-11-09T11:59:48Z","timestamp":1478692788000},"page":"68-84","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["On Classical Nonassociative Lambek Calculus"],"prefix":"10.1007","author":[{"given":"Wojciech","family":"Buszkowski","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,11,10]]},"reference":[{"key":"5_CR1","doi-asserted-by":"publisher","first-page":"1403","DOI":"10.2307\/2275485","volume":"56","author":"VM Abrusci","year":"1991","unstructured":"Abrusci, V.M.: Phase semantics and sequent calculus for pure noncommutative classical linear propositional logic. 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