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Two recent extension of the nonassociative Lambek calculus, the Lambek-Grishin calculus and the multimodal Lambek calculus, are shown to generate class of languages as tree adjoining grammars, using (tree generating) hyperedge replacement grammars as an intermediate step. As a consequence both extensions are mildly context-sensitive formalisms and benefit from polynomial parsing algorithms.dblp:conf/tag/Moot08 fatcat:7lzl7olsszghblld3ccjqpah3u