Lambek categorial grammars

The Lambek calculus and Lambek categorial grammars were introduced in 1958 for mathematical description of natural language syntax. In this approach, every word of the language is associated with (possibly several) syntactic categories (types) in a specific logical language, and then one checks derivability of the corresponding formula in the Lambek calculus. This formalism has several advantages in comparison with the Chomsky hierarchy (for example, context-free grammars), mainly the lexicalisation property: the syntactic information is kept in the categorial dictionary and used only if the corresponding word occurs in the text parsed. Categorial grammars also allow to do semantic analysis, using Montague semantics in a natural way. On the other hand, all the languages generated by Lambek categorial grammars are context-free. The talk will contain both the linguistic usage of categorial grammars and purely mathematical results concerning the Lambek calculus, including completeness results and algorithmic complexity.