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Syntactic Structures and the General Markov Models

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Abstract

We study phylogenetic signal present in syntactic information by considering the syntactic structures data from Longobardi (Linguist Anal 41:517–557, 2017), Collins (Syntactic structures of the world’s language: a cross-linguistic database. 27 September (2010), Colloquium: https://ling.yale.edu/syntactic-structures-worlds-language-cross-linguistic-database, 2010), Ceolin et al. (Front Psychol 11:2384, 2020) and Koopman (SSWL syntactic structures of the world’s languages: an open-ended database for the linguistic community and by the linguistic community. mit 50, 12. http://sswl.railsplayground.net/, 2011). Focusing first on the general Markov models, we explore how well the the syntactic structures data conform to the hypothesis required by these models. We do this by comparing derived phylogenetic trees against trees agreed on by the linguistics community. We then interpret the methods of Ceolin et al. (2020) as an infinite sites evolutionary model and compare the consistency of the data with this alternative. The ideas and methods discussed in the present paper are more generally applicable than to the specific setting of syntactic structures, and can be used in other contexts, when analyzing consistency of data with against hypothesized evolutionary models.

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Code/Data availability

The code and data used in this paper are available at https://github.com/minorllama/syntactic_structures_phylogenetics.

Notes

  1. The slight issue with negative determinants in Lake’s definition can be sidestepped using a constant scaling of the metric and moving it inside the logarithm.

  2. Rate matrix is any matrix where each row sums to zero, and all entries are positive off diagonal and non-positive on it; each edge is thought of as a continuous Markov chain associated to the rate matrix.

  3. In the updated SSWl Hittite has “11 Adposition Noun Phrase” set to value 0 and Armenian (Western Armenian) has “Neg 01 Standard Negation is Particle that Precedes the Verb” set to value 1.

  4. 01 Subject Verb, 06 Subject Object Verb, 11 Adposition Noun Phrase, 13 Adjective Noun, 15 Numeral Noun, 17 Demonstrative Noun, 19 Possessor Noun, 21 Pronominal Possessor Noun, Neg 03 Standard Negation is Prefix, Neg 08 Standard Negation is Tone plus Other Modification, Neg 10 Standard Negation is Infix, Neg 12 Distinct Negation of identity, Neg 13 Distinct Negation of Existence, Neg 14 Distinct Negation of Location, Order N3 01 Demonstrative Adjective Noun, Neg 04 Standard Negation is Suffix, 12 Noun Phrase Adposition.

  5. This convergence can be quantified with the Berry–Esseem theorem, see Durrett [13].

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Acknowledgements

We would like to thank the anonymous referees, and Andrea Ceolin for thoughtful feedback on the previous version of this paper that motivated this revision. The second author is partially supported by NSF grant DMS-2104330 and by FQXi grant FQXi-RFP-1 804 and Caltech’s Center for Evolutionary Science.

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  1. California Institute of Technology, Pasadena, USA

    Sitanshu Gakkhar & Matilde Marcolli

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  1. Sitanshu Gakkhar
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Gakkhar, S., Marcolli, M. Syntactic Structures and the General Markov Models. Math.Comput.Sci. 18, 4 (2024). https://doi.org/10.1007/s11786-023-00575-6

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