Lambek grammars with the unit. (English) Zbl 1370.03037
de Groote, Philippe (ed.) et al., Formal grammar. 15th and 16th international conferences, FG 2010, Copenhagen, Denmark, August 2010, FG 2011, Ljubljana, Slovenia, August 2011. Revised selected papers. Berlin: Springer (ISBN 978-3-642-32023-1/pbk). Lecture Notes in Computer Science 7395, 262-266 (2012).
Summary: 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.
For the entire collection see [Zbl 1248.68054].
For the entire collection see [Zbl 1248.68054].
MSC:
| 03B65 | Logic of natural languages |
| 03B47 | Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) |
