We propose a geometrical analysis of the principles that lay at the basis of categorial grammar and particularly of the Lambek calculus.
We argue that the basic properties of Residuation can be characterized in the framework of Cyclic Multiplicative Linear Logic (a purely non-commutative fragment of linear logic), by means of the classical proof nets that are defined in this system.
On this basis, a larger family of categorial grammar laws are analyzed: Monotonicity, Functional application, Type raising, Expansion.
The method we propose allows also to treat more complex principles such as Composition laws, Geach laws and Switching laws, obtaining interesting new possibilities implicit in these laws.
Joint work with V.M. Abrusci (Roma Tre, IT)