Lexicalization and Categorial Grammars - a Story Bar-hillel Might Have Liked

In the early 60’s Professor Bar-Hillel and his co-workers published a series of seminal papers on formal grammars, their mathematical properties and linguistic adequacy. Many of these papers appear in Bar-Hillel 1964. One of their papers was on categorial grammars and phrase structure grammars (Bar-Hillel, Galfman, and Shamir 1960). In this paper they showed that categorial grammars are weakly equivalent to context-free grammars. This was a period when any formal system that was shown to be equivalent or conjectured to be equivalent to CFG’s was put aside, as CFG’s were shown by Chomsky to be inadequate for the description of language. I suspect this was the reason why Bare-Hillel himself did not pursue the development of categorial grammars (see the last paragraph of Bax-Hillel, Gaifman and Shamir 1960).