Lambek grammars as combinatory categorial grammars
G Jager · Logic Journal of IGPL · 2001
We propose a combinatory reformulation of the product free version of the categorial calculus LL, i.e. the associative Lambek calculus that admits empty premises. We prove equivalence of the combinatory with the standard Natural Deduction presentation of LL. The result offers a new perspective on the relation between the type logical and the combinatory branch of the Categorial Grammar research program.