Pregroups and pregroup grammars were introduced in 1999 by Jim Lambek. He proposed that formalism as a new tool for syntactic analysis of natural languages. The formalism of pregroups belongs to the tradition of categorial grammars. In general they are part of a wide field of mathematical linguistics i.e. the theory of formal grammars and automata with applications in computer science.
Various aspects and properties of pregroups and pregroup grammars have been explored by logicians, mathematicians, linguists and computer scientists. The studies comprise axiomatization, constructing algorithms, exploring mathematical and computational properties and applying them to natural language processing. A number of authors have tried to modify the pure, initial calculus of pregroups in order to obtain some desired properties.
In this talk we want to make an overview of classical and extended pregroup grammars, compare different approaches and present their application to analyze formal and natural languages.