Abstract

The idea behind this line of research is applying mathematical structures, e.g. the ones used in arithmetic, to formalize grammar of natural languages. The early example of such an attempt is Lambek’s syntactic calculus in the 50’s. In the 90’s Lambek simplified his calculus and developed a novel mathematical structure which he called a Pregroup. Meanwhile, Pregroups have been applied to formalize the grammar of a wide range of natural languages, from English and French, to Japanese, Polish, and Persian. Independently, they have gained popularity in Physics and Computer Science communities where they are applied to reasoning about Quantum Protocols.

I will present recent joint work with Lambek and C. Casadio where we show how Pregroups can be extended with a simple rule to formalize, explain, and predict clitic and clitic-like movements in some natural languages. Based on our previous work on these languages, we observed that where one direction of the rule defines such movements in Persian, its converse is needed for French. Italian, on the other hand needs both of these directions, since it has both pre and post verbal clitics.