A tutorial on sentence semantics using lambek pregroup grammar and categorical quantum protocols

Abstract EN

Sentence semantics depends mainly on two basic principles: the principle of compositionality [Partee et al, 1990] (sometimes called Frege's principle), and the distributional principle.

Briefly, the compositionality principle states that the meaning of a complex expression is a function of the meaning of the parts and the syntactic rules by which they are combined.

The distributional principle is that words that occur in a similar context tend to have similar meaning [Turney and Pentel, 2010].

In this tutorial, the syntax used in compositionality is Lambek pregroup grammar [Lambek, 2006].

In order to integrate the above concepts together, categorical quantum protocols were used [Abramsky, and Coecke; 2004] to develop a categorical compositional distributional model of meaning [Grefenstette and Sadrzadeh, 2011][Coecke, et al, 2010] [Kartsaktis, 2014].

This model is sometimes abbreviated as DisCoCat model.

This tutorial gives outline for this model explaining the basic elements of the principles involved including Lambek pregroup grammar and categorical quantum protocols