Lecture Notes in Comput. Sci., 2012, Volume 7395, Pages 262–266
Lambek grammars with the unit
Department of Mathematical Logic and Theory of Algorithms,
Faculty of Mechanics and Mathematics, Moscow State University
Pentus’ theorem states that any language generated by a Lambek grammar is context-free. We present a substitution that reduces the Lambek calculus enriched with the unit constant to the variant of the Lambek calculus that does not contain the unit (but still allows empty premises), and use this substitution to prove that any language generated by a categorial grammar based on the Lambek calculus with the unit is context-free.
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