Mathematical Structure of Syntactic Merge

The syntactic Merge operation of the Minimalist Program in linguistics can be described mathematically in terms of Hopf algebras, with a formalism similar to the one arising in the physics of renormalization. This mathematical formulation of Merge has good descriptive power, as phenomena empirically observed in linguistics can be justified from simple mathematical arguments. It also provides a possible mathematical model for externalization and for the role of syntactic parameters.

Phylogenetics of Indo-European Language families via an Algebro-Geometric Analysis of their Syntactic Structures

Using Phylogenetic Algebraic Geometry, we analyze computationally the phylogenetic tree of subfamilies of the Indo-European language family, using data of syntactic structures. The two main sources of syntactic data are the SSWL database and Longobardi's recent data of syntactic parameters. We compute phylogenetic invariants and likelihood functions for two sets of Germanic languages, a set of Romance languages, a set of Slavic languages and a set of early Indo-European languages, and we compare the results with what is known through historical linguistics.