Topological Analysis of Syntactic Structures

Abstract

We use the persistent homology method of topological data analysis and dimensional analysis techniques to study data of syntactic structures of world languages. We analyze relations between syntactic parameters in terms of dimensionality, of hierarchical clustering structures, and of non-trivial loops. We show there are relations that hold across language families and additional relations that are family-specific. We then analyze the trees describing the merging structure of persistent connected components for languages in different language families and we show that they partly correlate to historical phylogenetic trees but with significant differences. We also show the existence of interesting non-trivial persistent first homology groups in various language families. We give examples where explicit generators for the persistent first homology can be identified, some of which appear to correspond to homoplasy phenomena, while others may have an explanation in terms of historical linguistics, corresponding to known cases of syntactic borrowing across different language subfamilies.

Syntactic structures and the general Markov models

“…This makes convergent evolution much less likely and is at odds with known historical phenomena of multiple reversals in some syntactic parameters. Further, in language evolution we do see homoplasy phenomena and horizontal transmission in syntax, as discussed for instance in Longobardi (2012) and detected through persistent first homology computation in Port et al (2019) and Port et al (2018).…”

“…For example, languages evolving in close geographic proximity as in the case of the microvariation phenomena studied in Guardiano et al (2016), represented in the data of Romance and Hellenic Southern Italian dialects in the LanGeLin data, can present more interaction than permitted by tree models. Known historical linguistic phenomena involving influences across different tree subbranches are well known at the lexical level (the Anglo-Norman bridge for example) but more rare at the syntactic level, although such structures are visible in the persistent first homology studied in Port et al (2019) and Port et al (2018) (the Gothic-Slavic-Hellenic loop discussed in Port et al (2019) for example). Such phenomena are beyond what is describable purely in terms of Markov models on trees.…”

“…As in Port et al (2019), we consider the languages belonging to the Uralic family (Estonian, Finnish, Hungarian, Udmurt, Yukaghir, Khanty) and to the more hypothetical Altaic family (Turkish, Buryat, Yakut, including the Tungusic languages Even and Evenki).…”

Natural language syntax complies with the free-energy principle

“…The model proposed in Gallego and Orús ( 2022 , p. 20) assumes that language is “the cheapest non-trivial computational system”, exhibiting a high degree of efficiency with respect to its MERGE-based coarse-graining. More recently, MERGE has been described mathematically in terms of Hopf algebras, with a formalism similar to the one arising in the physics of renormalization (Marcolli et al, 2023 ), and the persistent homology method of topological data analysis and dimensional analysis techniques has been used to study syntactic parameters (Port et al, 2022 ). Hence, both the computational and mathematical foundations of syntax can be cast in ways that directly accord with the demands of the FEP and active inference.…”

Syntactic Structures and the General Markov Models

“…Our goal is to investigate how well the model describes the evolutionary processes on natural language syntax, at the same time comparing the phylogenetic signal we obtain to that of Ceolin et al (2020). We also explore the question of metricizing the space of syntactic structures that is relevant to the persistent homology machinery used by Port et al (2019) towards questions on the phylogenetics of language families.…”