Phylogenetics of Indo-European Language Families via an Algebro-Geometric Analysis of Their Syntactic Structures

Abstract

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 estimates of the Euclidean distance 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.

Syntactic structures and the general Markov models

“…With Slovenian excluded, all three Longobardi et al (2013); Shu et al (2017); Nurbakova et al (2013) agree on this tree. The reconstruction is robust: with approximately 60% of the parameters sampled uniformly randomly, this topology appears with a probability in excess of 0.6.…”

“…Such phenomena are beyond what is describable purely in terms of Markov models on trees. Moreover, different syntactic parameters are not independent variables: some relations are explicitly known (as discussed in Longobardi and Guardiano (2009), Longobardi (2017a) for instance), while other relations can be detected through methods of data analysis, as in Ortegaray et al (2018), Park et al (2017), or through methods of coding theory Shu and Marcolli (2017), Marcolli (2016). The presence of dependencies between syntactic parameters violates the Markov models on trees hypothesis that these variables can be treated as identically distributed independent random variables.…”

“…There was some debate in recent years in the linguistic community (see Perelysvaig and Lewis (2015)) around computational reconstructions of the structure of the Indo-European tree near the root. In particular, this subset of languages was chosen in Shu et al (2017) in order to compare the relative positions of the Anatolian and Tocharian branches and the Albanian, Armenian, and Hellenic branches, between two candidate trees, one obtained in Bouckaert et al (2012) on the basis of lexical data and one, generally regarded by linguists as more reliable, obtained in Ringe et al (2002) including morphological data. The phylogenetic algebraic geometry method, applied in Shu et al (2017) to the SSWL syntactic data for this set of languages, slightly favors the tree of Ringe et al (2002).…”

“…The Rexová et al (2003) construction is based on lexicographic data, like the tree of Bouckaert et al (2012), while the tree of Ringe et al (2002) includes both lexicographic and morphological data. None of these previous analyses, with the exception of Shu et al (2017), are based on syntactic parameters, so the syntactic input can be seen as an independent verification. We find that the tree of Rexova et al lies between the tree of Bouckaert et al, and that of Ringe et al when evaluated with phylogenetic invariants: Shu et al (2017) compares T 1 of Bouckaert et al (2012) and T 2 Ringe et al (2002), computing T 3 invariants (on rolled back parameter data) yields…”

Using Cross-Lingual Part of Speech Tagging for Partially Reconstructing the Classic Language Family Tree Model

“…The same method was re-used in (Longobardi et al, 2013), which was concluded in a similar way. In a recent work, Shu et al (2021) applied a different comparison technique on the same syntactic characteristics, using Markov models. In all of those works, the selection of the syntactic characteristics to be used for comparison, plays an important role in the creation of a language proximity model.…”