Chapter published in:
The Determinants of Diachronic Stability
Edited by Anne Breitbarth, Miriam Bouzouita, Lieven Danckaert and Melissa Farasyn
[Linguistik Aktuell/Linguistics Today 254] 2019
► pp. 263–290

Chapter 11
Stable variation in multidimensional competition

| The University of Manchester
The Fundamental Theorem of Language Change (Yang 2000) implies the impossibility of stable variation in the Variational Learning framework, but only in the special case where two, and not more, grammatical variants compete. Introducing the notion of an advantage matrix, I generalize Variational Learn-ing to situations where the learner receives input generated by more than two grammars, and show that diachronically stable variation is an intrinsic feature of several types of such multiple-grammar systems. This invites experimentalists to take the possibility of stable variation seriously and identifies one possible place where to look for it: situations of complex language contact.
Article outline
  • 1.Variation, learning and diachronic stability
  • 2.Two grammars
  • 3.Advantage matrices and the cyclical balance criterion
  • 4.Dynamics: General results
  • 5.Babelian systems
  • 6.Symmetric systems
  • 7.Quasi-Babelian systems
  • 8.Naive learning
  • 9.Conclusions and conjectures
  • Acknowledgements
  • Notes
  • References
Published online: 20 March 2019
https://doi.org/10.1075/la.254.11kau
References
Aronoff, Mark
1976 Word Formation in Generative Grammar. Cambridge MA: The MIT Press.Google Scholar
Bartol Jr., Thomas M., Bromer, Cailey, Kinney, Justin, Chirillo, Michael A., Bourne, Jennifer N., Harris, Kristen M. & Sejnowski, Terrence J.
2015 Nanoconnectomic upper bound on the variability of synaptic plasticity. eLife 4: 10778. CrossrefGoogle Scholar
Bush, Robert R. & Mosteller, Frederick
1955 Stochastic Models for Learning. New York NY: Wiley. CrossrefGoogle Scholar
Drazin, Philip Gerald
1992 Nonlinear Systems. Cambridge: CUP. CrossrefGoogle Scholar
Gold, E. Mark
1967 Language identification in the limit. Information and Control 10: 447–474. CrossrefGoogle Scholar
Kauhanen, Henri
2018 Individual and Population in Language Change: Mathematical Explorations of the Acquisition-Use Loop. PhD dissertation, The University of Manchester.Google Scholar
Kroch, Anthony
1994 Morphosyntactic variation. In Papers from the 30th Regional Meeting of the Chicago Linguistic Society: Parasession on Variation and Linguistic Theory, Katharine Beals et al.. (eds), 180–201. Chicago IL: CLS.Google Scholar
Longobardi, Giuseppe & Guardiano, Cristina
2009 Evidence for syntax as a signal of historical relatedness. Lingua 199: 1679–1706. CrossrefGoogle Scholar
Narendra, Kumpati S. & Thathachar, Mandayam A. L.
1989 Learning Automata: An Introduction. Englewood Cliffs NJ: Prentice-Hall.Google Scholar
Niyogi, Partha
2002 The computational study of diachronic linguistics. In Syntactic Effects of Morphological Change, David W. Lightfoot (ed), 351–365. Oxford: OUP. CrossrefGoogle Scholar
Wallenberg, Joel C.
2016 Extraposition is disappearing. Language 92: e237–e256. CrossrefGoogle Scholar
Yang, Charles D.
1999 A selectionist theory of language acquisition. In Proceedings of the 37th Annual Meeting of the Association for Computational Linguistics, 429–435. Stroudsburg PA: ACL.Google Scholar
2000 Internal and external forces in language change. Language Variation and Change 12: 231–250. CrossrefGoogle Scholar
2002a Grammar competition and language change. In Syntactic Effects of Morphological Change, David W. Lightfoot (ed.), 367–380. Oxford: OUP. CrossrefGoogle Scholar
2002b Knowledge and Learning in Natural Language. Oxford: OUP.Google Scholar
2004 Universal Grammar, statistics or both? Trends in Cognitive Sciences 8: 451–456. CrossrefGoogle Scholar