Extending Lambek grammars to basic categorial grammars

Pentus (1992) proves the equivalence of LCG's and CFG's, and CFG's are equivalent to BCG's by the Gaifman theorem (Bar-Hillel et al., 1960). This paper provides a procedure to extend any LCG to an equivalent BCG by affixing new types to the lexicon; a procedure of that kind was proposed as early, as Cohen (1967), but it was deficient (Buszkowski, 1985). We use a modification of Pentus' proof and a new proof of the Gaifman theorem on the basis of the Lambek calculus.