Formalizing natural language grammar: the Lambek syntactic calculus and its algebraic models

We study the properties of Lambek's syntactic calculus and establish an axiomatic system that guarantees a decision procedure for determining whether a string of words belonging to given types is a complete declarative sentence or not. Our aim is to establish a mathematical decision procedure to test whether the grammatical or not of a given sentence is complete. We will try to induce some simple rules from the English grammar and we will check if they are confirmed by the different computational methods. The results show that the pregroup model offers a simpler and intuitive solution to linguistic questions.