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

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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.

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References

  1. Allman, E., Rhodes, J.: Phylogenetic ideals and varieties for general Markov models. Adv. Appl. Math. 40, 127–148 (2008)

    Article  MathSciNet  Google Scholar 

  2. Anthony, D.W., Ringe, D.: The Indo-European homeland from linguistic and archaeological perspectives. Annu. Rev. Linguist. 1, 199–219 (2015)

    Article  Google Scholar 

  3. Baker, M.: The Atoms of Language. Basic Books, New York (2001)

    Google Scholar 

  4. Barbançon, F., Evans, S.N., Nakhleh, L., Ringe, D., Warnow, T.: An experimental study comparing linguistic phylogenetic reconstruction methods. Diachronica 30(2), 143–170 (2013)

    Article  Google Scholar 

  5. Bocci, C.: Topics in phylogenetic algebraic geometry. Expo. Math. 25, 235–259 (2007)

    Article  MathSciNet  Google Scholar 

  6. Bouckaert, R., Lemey, P., Dunn, M., Greenhill, S.J., Alekseyenko, A.V., Drummond, A.J., Gray, R.D., Suchard, M.A., Atkinson, Q.D.: Mapping the origins and expansion of the Indo-European language family. Science 337, 957–960 (2012)

    Article  Google Scholar 

  7. Bruns, W., Vetter, U.: Determinantal Rings. Lecture Notes in Mathematics, vol. 1327. Springer, Berlin (1988)

    Book  Google Scholar 

  8. Casanellas, M., Fernández-Sánchez, J.: Performance of a new invariants method on homogeneous and nonhomogeneous quartet trees. Mol. Biol. Evol. 24(1), 288–293 (2007)

    Article  Google Scholar 

  9. Cartwright, D., Häbich, M., Sturmfels, B., Werner, A.: Mustafin varieties. Selecta Math. (N.S.) 17(4), 757–793 (2011)

    Article  MathSciNet  Google Scholar 

  10. Chomsky, N.: Lectures on Government and Binding. Foris Publications, Dordrecht (1982)

    Google Scholar 

  11. Chomsky, N.: The Minimalist Program, 20th, Anniversary MIT Press (2015)

  12. Chomsky, N., Lasnik, H.: The theory of Principles and Parameters. In: Syntax: An International Handbook of Contemporary Research, pp. 506–569, de Gruyter, (1993)

  13. Draisma, J., Horobeţ, E., Ottaviani, G., Sturmfels, B., Thomas, R.: The Euclidean distance degree of an algebraic variety. Found. Comput. Math. 16(1), 99–149 (2016)

    Article  MathSciNet  Google Scholar 

  14. Eriksson, N.: Using invariants for phylogenetic tree construction. In: Emerging Applications of Algebraic Geometry, IMA Volumes in Mathematics and Its Applications, vol. 149, pp. 89–108. Springer (2009)

  15. Eriksson, N., Ranestad, K., Sturmfels, B., Sullivant, S.: Phylogenetic Algebraic Geometry. In: Projective Varieties with Unexpected Properties, pp. 237–255. Walter de Gruyter (2005)

  16. Forster, P., Renfrew, C.: Phylogenetic Methods and the Prehistory of Language. McDonald Institute Monographs, Cambridge (2006)

    Google Scholar 

  17. Gakkhar, S., Marcolli, M.: Syntactic structures and the general Markov model, in preparation

  18. Gray, R.D., Atkinson, Q.D.: Language-tree divergence times support the Anatolian theory of Indo-European origin. Nature 426(6965), 435–439 (2003)

    Article  Google Scholar 

  19. Gusfield, D.: Recombinatorics. MIT Press, Cambridge (2014)

    Book  Google Scholar 

  20. Harris, J.: Algebraic Geometry. Springer, Berlin (2013)

    Google Scholar 

  21. Kazakov, D., Cordoni, G., Algahtani, E., Ceolin, A., Irimia, M., Kim, S.S., Michelioudakis, D., Radkevich, N., Guardiano, C., Longobardi, G.: Learning implicational models of Universal Grammar parameters. In: EVOLANG XII, pp. 16–19 April 2018, Torun, Poland

  22. Karimi, S., Piattelli-Palmarini M. (eds.): Special Issue on Parameters, Linguistic Analysis, vol. 41, No. 3–4 (2017)

  23. Hauenstein, J., Rodriguez, J.I., Sturmfels, B.: Maximum likelihood for matrices with rank constraints. J. Algebr. Stat. 5(1), 18–38 (2014)

    Article  MathSciNet  Google Scholar 

  24. Longobardi, G.: Principles, parameters, and schemata. A constructivist UG. Linguist. Anal. 41(3–4), 517–556 (2017)

    Google Scholar 

  25. Longobardi, G.: A minimalist program for parametric linguistics? In: Broekhuis, H., Corver, N., Huybregts, M., Kleinhenz, U., Koster, J. (eds.) Organizing Grammar: Linguistic Studies for Henk van Riemsdijk, pp. 407–414. Mouton de Gruyter, Berlin (2005)

    Google Scholar 

  26. Longobardi, G.: Methods in parametric linguistics and cognitive history. Linguist. Var. Yearb. 3, 101–138 (2003)

    Article  Google Scholar 

  27. Longobardi, G., Guardiano, C.: Evidence for syntax as a signal of historical relatedness. Lingua 119, 1679–1706 (2009)

    Article  Google Scholar 

  28. Longobardi, G., Guardiano, C., Silvestri, G., Boattini, A., Ceolin, A.: Towards a syntactic phylogeny of modern Indo-European languages. J. Hist. Linguist. 3(1), 122–152 (2013)

    Article  Google Scholar 

  29. Longobardi, G., Buch, A., Ceolin, A., Ecay, A., Guardiano, C., Irimia, M., Michelioudakis, D., Radkevich, N., Jaeger, G.: Correlated evolution or not? phylogenetic linguistics with syntactic, cognacy, and phonetic data. In: Roberts, S.G. et al. (eds.) The Evolution of Language: Proceedings of the 11th International Conference (EVOLANGX11), 2016 Online at http://evolang.org/neworleans/papers/162.html. (2016)

  30. Marcolli, M.: Syntactic parameters and a coding theory perspective on entropy and complexity of language families. Entropy 18(4), 110 (2016)

    Article  MathSciNet  Google Scholar 

  31. Mirsky, L.: Symmetric gauge functions and unitarily invariant norms. Q. J. Math. 11, 1156–1159 (1966)

    Google Scholar 

  32. Murawaki, Y.: Continuous space representations of linguistic typology and their application to phylogenetic inference. In: Human Language Technologies: The 2015 Annual Conference of the North American Chapter of the ACL, pp. 324–334 (2015)

  33. Nakhleh, L., Ringe, D., Warnow, T.: Perfect phylogenetic networks: a new methodology for reconstructing the evolutionary history of natural languages. Language 81(2), 382–420 (2005)

    Article  Google Scholar 

  34. Ortegaray, A., Berwick, R.C., Marcolli, M.: Heat kernel analysis of syntactic structures. arXiv:1803.09832, to appear in Mathematics in Computer Science

  35. Pachter, L., Sturmfels, B.: The mathematics of phylogenomics. SIAM Rev. 49(1), 3–31 (2007)

    Article  MathSciNet  Google Scholar 

  36. Pachter, L., Sturmfels, B.: Tropical geometry of statistical models. Proc. Natl. Acad. Sci. (PNAS) 101(46), 16132–16137 (2004)

    Article  MathSciNet  Google Scholar 

  37. Pachter, L., Sturmfels, B.: Algebraic Statistics for Computational Biology. Cambridge University Press, Cambridge (2005)

    Book  Google Scholar 

  38. Park, J.J., Boettcher, R., Zhao, A., Mun, A., Yuh, K., Kumar, V., Marcolli, M.: Prevalence and recoverability of syntactic parameters in sparse distributed memories. In: Geometric Science of Information. Third International Conference GSI 2017, Lecture Notes in Computer Science, vol. 10589, pp. 265–272. Springer (2017)

  39. Perelysvaig, A., Lewis, M.W.: The Indo-European Controversy: Facts and Fallacies in Historical Linguistics. Cambridge University Press, Cambridge (2015)

    Book  Google Scholar 

  40. PHYLIP: http://evolution.genetics.washington.edu/phylip.html

  41. Port, A., Gheorghita, I., Guth, D., Clark, J.M., Liang, C., Dasu, S., Marcolli, M.: Persistent topology of syntax. Math. Comput. Sci. 12(1), 33–50 (2018)

    Article  MathSciNet  Google Scholar 

  42. Port, A., Karidi, T., Marcolli, M.: Topological analysis of syntactic structures. arXiv:1903.05181

  43. Ringe, D., Warnow, T., Taylor, A.: Indo-European and computational cladistics. Trans. Philol. Soc. 100, 59–129 (2002)

    Article  Google Scholar 

  44. Rizzi, L.: On the format and locus of parameters: the role of morphosyntactic features. Linguist. Anal. 41, 159–191 (2017)

    Google Scholar 

  45. Rusinko, J.P., Hipp, B.: Invariant based quartet puzzling. Algorithms Mol. Biol. 7, 35 (2012)

    Article  Google Scholar 

  46. Shu, K., Marcolli, M.: Syntactic structures and code parameters. Math. Comput. Sci. 11(1), 79–90 (2017)

    Article  MathSciNet  Google Scholar 

  47. Shu, K., Aziz, S., Huynh, V.L., Warrick, D., Marcolli, M.: Syntactic phylogenetic trees. In: Kouneiher, J. (ed.) Foundations of Mathematics and Physics one Century After Hilbert, pp. 417–441. Springer, Berlin (2018)

    Chapter  Google Scholar 

  48. Siva, K., Tao, J., Marcolli, M.: Spin glass models of syntax and language evolution. Linguist. Anal. 41(3–4), 559–608 (2017)

    Google Scholar 

  49. SSWL Database of Syntactic Parameters: http://sswl.railsplayground.net/

  50. Sturmfels, B., Sullivant, S.: Toric ideals of phylogenetic invariants. J. Comput. Biol. 12(2), 204–228 (2005)

    Article  Google Scholar 

  51. Warnow, T.: Computational Phylogenetics. Cambridge University Press, Cambridge (2017)

    Book  Google Scholar 

  52. Warnow, T., Evans, S.N., Ringe, D., Nakhleh, L.: Stochastic models of language evolution and an application to the Indo-European family of languages. Available at http://www.stat.berkeley.edu/users/evans/659.pdf

Download references

Acknowledgements

The first and second author were partially supported by a Summer Undergraduate Research Fellowship at Caltech. The last author is partially supported by NSF Grant DMS-1707882, NSERC Discovery Grant RGPIN-2018-04937, Accelerator Supplement Grant RGPAS-2018-522593, and by the Perimeter Institute for Theoretical Physics. We are very grateful to the two anonymous referees for many very useful comments, corrections, and suggestions that greatly improved the paper.

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Authors and Affiliations

  1. California Institute of Technology, Pasadena, USA

    Kevin Shu, Andrew Ortegaray & Matilde Marcolli

  2. Massachusetts Institute of Technology, Cambridge, USA

    Robert C. Berwick

  3. Perimeter Institute for Theoretical Physics, Waterloo, Canada

    Matilde Marcolli

  4. University of Toronto, Toronto, Canada

    Matilde Marcolli

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  1. Kevin Shu
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Appendices

Appendix A: SSWL Syntactic Variables of the Set \(\mathcal {S}_1(G)\) of Germanic Languages

We list here the 90 binary syntactic variables of the SSWL database that are completely mapped for the six Germanic languages \(\ell _1\,=\,\)Dutch, \(\ell _2\,=\,\)German, \(\ell _3\,=\,\)English, \(\ell _4\,=\,\)Faroese, \(\ell _5\,=\,\)Icelandic, \(\ell _6\,=\,\)Swedish. The column on the left in the tables lists the SSWL parameters P as labeled in the database.

figure w

Appendix B: SSWL Syntactic Variables of the Set \(\mathcal {S}_2(G)\) of Germanic Languages

We list here the 90 binary syntactic variables of the SSWL database that are completely mapped for the seven Germanic languages \(\ell _1\,=\,\)Norwegian, \(\ell _2\,=\,\)Danish, \(\ell _3\,=\,\)Gothic, \(\ell _4\,=\,\)Old English, \(\ell _5\,=\,\)Icelandic, \(\ell _6\,=\,\)English, \(\ell _7\,=\,\)German. The column on the left in the tables lists the SSWL parameters P as labeled in the database.

figure x

Appendix C: Flattening Matrices \(F_5\) and \(F_6\)

The flattening matrices of (3.1) (written in transpose form for convenience) for the \(T_5\) and \(T_6\) trees, in the case of the Longobardi data are given by the following:

$$\begin{aligned} F_5^t = \left( \begin{array}{cccc} \frac{4}{7} &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} \frac{1}{42} \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} \frac{1}{42} \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} \frac{1}{42} &{} 0 &{} \frac{1}{42} \\ 0 &{} 0 &{} 0 &{} \frac{1}{42} \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} \frac{1}{42} &{} \frac{2}{7} \end{array} \right) \ \ \ \ \ F_6^t = \left( \begin{array}{cccc} \frac{4}{7} &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} \frac{1}{42} \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} \frac{1}{42} \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} \frac{1}{42} &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} \frac{1}{42} \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} \frac{1}{42} &{} \frac{1}{42} &{} \frac{2}{7} \end{array} \right) \end{aligned}$$

The same flattening matrices of (3.1) for the SSWL data are given by the following.

$$\begin{aligned} F_5^t = \left( \begin{array}{cccc} \frac{13}{34} &{} \frac{1}{68} &{} \frac{1}{34} &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} \frac{1}{68} &{} 0 \\ \frac{3}{68} &{} \frac{1}{68} &{} \frac{1}{68} &{} \frac{1}{68} \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} \frac{1}{68} \\ 0 &{} 0 &{} 0 &{} \frac{1}{68} \\ \frac{1}{68} &{} 0&{}0&{}0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} \frac{1}{68} \\ 0 &{} 0 &{} \frac{1}{34} &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} \frac{1}{68} \\ \frac{1}{68} &{} 0&{}0&{}0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} \frac{1}{68} \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} \frac{1}{68} &{} \frac{1}{34} &{} \frac{1}{68} \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} \frac{3}{68} &{} \frac{4}{17} \end{array} \right) \ \ \ \ \ F_6^t = \left( \begin{array}{cccc} \frac{13}{34} &{} \frac{1}{68} &{} \frac{3}{68} &{} \frac{1}{68} \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ \frac{1}{34} &{} 0 &{} \frac{1}{68} &{} \frac{1}{68} \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} \frac{1}{68} \\ \frac{1}{68} &{} 0 &{} 0 &{} \frac{1}{68} \\ \frac{1}{68} &{} 0&{}0&{}0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} \frac{1}{34} &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} \frac{1}{68} &{} 0 &{} \frac{1}{68} \\ \frac{1}{68} &{} 0&{}0&{}0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} \frac{1}{68} \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} \frac{1}{68} &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 0 \\ \frac{1}{34} &{} \frac{1}{68} &{} \frac{3}{68} &{} \frac{4}{17} \end{array} \right) \end{aligned}$$

Appendix D: List of LanGeLin Syntactic Parameters

FGP

Gramm. person

GSI

Grammaticalised inalienability

FGM

Gramm. Case

ALP

Alienable possession

FPC

Gramm. perception

GST

Grammaticalised Genitive

FGT

Gramm. temporality

GEI

Genitive inversion

FGN

Gramm. number

GNR

Non-referential head marking

GCO

Gramm. collective number

STC

Structured cardinals

PLS

Plurality spreading

GPC

Gender polarity cardinals

FND

Number in D

PMN

Personal marking on numerals

FSN

Feature spread on N

CQU

Cardinal quantifiers

FNN

Number in N

PCA

Number spread through cardinal adjectives

SGE

Semantic gender

PSC

Number spread from cardinal quantifiers

FGG

Gramm. gender

RHM

Head-markong on Rel

CGB

Unbounded sg N

FRC

Verbal relative clauses

DGR

Gramm. amount

NRC

Nominalized relative clause

DGP

Gramm. text anaphora

NOR

NP over verbal rel clauses/adpos gen

CGR

Strong amount

AER

Relative extrap.

NSD

Strong person

ARR

Free reduced rel

FVP

Variable person

DOR

def on relatives

DGD

Gramm. distality

NOD

NP over D

DPQ

Free null partitive Q

NOP

NP over non-genitive arguments

DCN

Article-checking N

PNP

P over complement

DNN

Null-N-licensing art

NPP

N-raising with obl. pied-piping

DIN

D-controlled infl. on N

NGO

N over GenO

FGC

Gramm. classifier

NOA

N over As

DBC

Strong classifier

NM2

N over M2 As

XCN

Conjugated nouns

NM1

N over M1 As

GSC

c-selection

EAF

Fronted high As

NOE

N over ext. arg.

NON

N over numerals

HMP

NP-heading modifier

FPO

Feature spread to genitive postpositions

AST

Structured APs

ACM

Class MOD

FFS

Feature spread to struct. APs

DOA

def on all +N

ADI

D-controlled infl. on A

NEX

Gramm. expletive article

DMP

def matching pron. poss.

NCL

Clitic poss.

DMG

def matching genitives

PDC

Article-checking poss.

GCN

Poss\(^o\)-checking N

ACL

Enclitic poss. on As

GFN

Gen-feature spread to Poss\(^o\)

APO

Adjectival poss.

GAL

Dependent Case in NP

WAP

Wackernagel adjectival poss.

GUN

Uniform Gen

AGE

Adjectival Gen

EZ1

Generalized linker

OPK

Obligatory possessive with kinship noun

EZ2

Non-clausal linker

TSP

Split deictic demonstratives

EZ3

Non-genitive linker

TSD

Split demonstratives

GAD

Adpositional Gen

TAD

Adjectival demonstratives

GFO

GenO

TDC

Article-checking demonstratives

PGO

Partial GenO

TLC

Loc-checking demonstratives

GFS

GenS

TNL

NP over Loc

GIT

Genitive-licensing iterator

  

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Shu, K., Ortegaray, A., Berwick, R.C. et al. Phylogenetics of Indo-European Language Families via an Algebro-Geometric Analysis of Their Syntactic Structures. Math.Comput.Sci. 15, 803–857 (2021). https://doi.org/10.1007/s11786-021-00507-2

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