On translating context-free grammars into Lambek grammars

We consider context-free grammars and Lambek grammars enriched with semantic labeling. Such grammars do not just answer whether a given word belongs to the language described by the grammar, but, if the answer is positive, also assign the word a $\lambda $-term that corresponds to the semantic value (“meaning”) of the word. We present a modification of W. Buszkowski's direct translation of context-free grammars in the Chomsky normal form into Lambek grammars; this modification preserves semantic values of words.