A Geometrical Representation of the Basic Laws of Categorial Grammar

We present a geometrical analysis of the principles that lay at the basis of Categorial Grammar and of the Lambek Calculus. In Abrusci (On residuation, 2014) it is shown that the basic properties known as Residuation laws can be characterized in the framework of Cyclic Multiplicative Linear Logic, a purely non-commutative fragment of Linear Logic. We present a summary of this result and, pursuing this line of investigation, we analyze a well-known set of categorial grammar laws: Monotonicity, Application, Expansion, Type-raising, Composition, Geach laws and Switching laws.

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