Dependency-based analyses for function words. Introducing the polygraphic approach

This paper scrutinizes various dependency-based representations of the syntax of function words, such as prepositions. The focus is on the underlying formal object used to encode the linguistic analyses and its relation to the corresponding linguistic theory. Two types of representation are proposed for the encoding of syntactic properties and applied for function words. Although the mathematical object introduced here encodes a dependency-based analysis, it does not consist in a tree. It is rather more general than a graph (it allows edges to be vertices of other edges) and is called a polygraph.