I present a geometrical analysis – i.e. by means of proof nets of the multiplicative fragment of Cyclic Linear Logic - of the principles that lay at the basis of Categorial Grammar and of the Lambek Calculus: Residuation laws, Monotonicity laws, Application laws, Expansion laws, Type-raising laws, Composition laws, Geach laws and Switching laws. This geometrical analysis leads to better understand these laws, and to discover some laws have a common geometrical representation (the proofs of Application laws, Expansion Laws and Type-reasing laws are represented by proof-nets with two axiom links, whereas the proofs of Composition laws, Geach laws and Switching laws are represented by proof-nets with three axiom links). The talk is based on a joint work with Claudia Casadio.
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