Lambek Grammars with the Unit
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.
Unable to display preview. Download preview PDF.
- Kuznetsov, S.: Lambek grammars with one division and one primitive type. Unpublished manuscript (2010)Google Scholar