, Volume 27, Issue 4, pp 497–526 | Cite as

The grammaticalization cycle of the progressive

A game-theoretic analysis
  • Roland MühlenberndEmail author
  • Dankmar Enke


A well-attested phenomenon in morpho-semantic change is known as the progressive cycle, which depicts a directed and cyclic pathway of a grammatical progressive marker through its emergence and disappearance inside the imperfective domain. Deo (2015) offers a model within the framework of evolutionary game theory to study the evolutionary dynamics of four preselected types of progressive-imperfective grammars. Based on her basic game-theoretic model, we investigate which types of grammars would emerge from the first principles in a population of agents under reinforcement learning. In our computational model, the actual progressive-imperfective cycle can be reconstructed from such atomic interactions between learner agents after the addition of several simple assumptions to the basic game-theoretic model.


Morpho-semantic change Progressive cycle Evolutionary dynamics Game theory Reinforcement learning 


  1. Aarts, B., Close, J., & Wallis, S. (2010). Recent changes in the use of the progressive construction in English. In B. Cappelle & N. Wada (Eds.), Distinctions in English grammar (pp. 148–167). Tokyo: Kaitakusha. Google Scholar
  2. Ahern, C., & Clark, R. (2014). Diachronic processes in language as signaling under conflicting interests. In E. Cartmill (Ed.), The evolution of language: proceedings of the tenth international conference on the evolution of language (pp. 25–32). Singapore: World Scientific. CrossRefGoogle Scholar
  3. Argiento, R., Pemantle, R., Skyrms, B., & Volkov, S. (2009). Learning to signal: analysis of a micro-level Reinforcement model. Stochastic Processes and their Applications, 119, 373–390. CrossRefGoogle Scholar
  4. Ashton, E. (1949). Swahili grammar. London: Longman. Google Scholar
  5. Barrett, J. A. (2006). Numerical simulations of the Lewis signaling game: learning strategies, pooling equilibria, and the evolution of grammar. Irvine: University of California. Technical Report MBS 06-09, Institute for Mathematical Behavioral Science. Google Scholar
  6. Bonami, O. (2015). Periphrasis as collocation. Morphology, 25(1), 63–110. CrossRefGoogle Scholar
  7. Börgers, T., & Sarin, R. (1997). Learning through reinforcement and replicator dynamics. Journal of Economic Theory, 77(1), 1–14. CrossRefGoogle Scholar
  8. Brown, D., Chumakina, M., Corbett, G., Popova, G., & Spencer, A. (2012). Defining ‘periphrasis’: key notions. Morphology, 22(2), 233–275. CrossRefGoogle Scholar
  9. Bush, R., & Mosteller, F. (1955). Stochastic models for learning. New York, NY: Wiley. CrossRefGoogle Scholar
  10. Bybee, J., Perkins, R., & Pagliuca, W. (1994). The evolution of grammar. Tense, aspect, and modality in the languages of the world. Chicago: Chicago University Press. Google Scholar
  11. Cangelosi, A., & Parisi, D. (1998). The emergence of a ‘language’ in an evolving population of neural networks. Connection Science, 10(2), 83–97. CrossRefGoogle Scholar
  12. Comrie, B. (1976). Aspect. Cambridge: Cambridge University Press. Google Scholar
  13. Dahl, Ö. (1979). Typology of sentence negation. Linguistics, 17(1–2), 79–106. Google Scholar
  14. Dahl, Ö. (1985). Tense and aspect systems. Oxford: Blackwell. Google Scholar
  15. Deo, A. (2006). Tense and aspect in Indo-Aryan languages: variation and diachrony. Doctoral dissertation, Stanford University. Google Scholar
  16. Deo, A. (2015). The semantic and pragmatic underpinnings of grammaticalization paths: the progressive to imperfective shift. Semantics and Pragmatics, 8, 1–52, article 14. CrossRefGoogle Scholar
  17. Ebert, K. (2000). Progressive markers in the Germanic languages. In O. Dahl (Ed.), Tense and aspect in the languages of Europe (pp. 605–653). Berlin: de Gruyter. Google Scholar
  18. Enke, D., Mühlenbernd, R., & Yanovich, I. (2016). The emergence of the progressive to imperfective diachronic cycle in reinforcement-learning agents. In S. Roberts, C. Cuskley, L. McCrohon, L. Barceló-Coblijn, O. Feher, & T. Verhoef (Eds.), Proceedings of the 11th international conference on the evolution of language (Evolang 11). Google Scholar
  19. Fagyal, Z., Swarup, S., Escobar, A. M., Gasser, L., & Lakkaraju, K. (2010). Centers and peripheries: network roles in language change. Lingua, 120, 2061–2079. CrossRefGoogle Scholar
  20. Göksel, A., & Kerslake, C. (2015). Turkish: a comprehensive grammar. London: Routledge. Google Scholar
  21. Goldsmith, J., & Woisetschlaeger, E. (1982). The logic of the English progressive. Linguistic Inquiry, 13(1), 79–89. Google Scholar
  22. Hellinger, E. (1909). Neue Begründung der Theorie quadratischer Formen von unendlichvielen Veränderlichen. Journal für die reine und angewandte Mathematik, 136, 210–271. Google Scholar
  23. Horn, L. (1984). Towards a new taxonomy of pragmatic inference: Q-based and R-based implicature. In D. Schiffrin (Ed.), Meaning, form, and use in context: linguistic applications (pp. 11–42). Washington: Georgetown University Press. Google Scholar
  24. Huttegger, S. M. (2007). Evolution and the explanation of meaning. Philosophy of Science, 74(1), 1–27. CrossRefGoogle Scholar
  25. Huttegger, S. M., & Zollman, K. J. S. (2011). Signaling games: dynamics of evolution and learning. In A. Benz, C. Ebert, G. Jäger, & R. van Rooij (Eds.), Language, games, and evolution (pp. 160–176). Berlin: Springer. CrossRefGoogle Scholar
  26. Jäger, G. (2004). Evolutionary game theory for linguists (Tech. Rep.). Stanford, University and University of Potsdam. Google Scholar
  27. Jäger, G. (2007). Evolutionary game theory and typology: a case study. Language, 83(1), 74–109. CrossRefGoogle Scholar
  28. Jäger, G. (2014). What is a universal? On the explanatory potential of evolutionary game theory in linguistics. In E. McCready, K. Yabushita, & K. Yoshimoto (Eds.), Formal approaches to semantics and pragmatics (pp. 85–103). Dordrecht: Springer. Google Scholar
  29. Ke, J., Gong, T., & Wang, W. S.-Y. (2008). Language change and social networks. Communications in Computational Physics, 3(4), 935–949. Google Scholar
  30. Kirby, S. (2005). The evolution of meaning-space structure through iterated learning. In A. Cangelosi & C. Nehaniv (Eds.), Second international symposium on the emergence and evolution of linguistic communication (pp. 56–63). Google Scholar
  31. Kirby, S., & Hurford, J. (1997). Learning, culture and evolution in the origin of linguistic constraints. In P. Husbands & I. Harvey (Eds.), Proceedings of the fourth European conference on artificial life (pp. 493–502). Cambridge: MIT Press. Google Scholar
  32. Lewis, D. (1969). Convention. Cambridge: Harvard University Press. Google Scholar
  33. Li, P., Maher, S., Newmark, E., & Hurley, J. (2001). The role of parental input in the acquisition of tense-aspect morphology. Journal of Cognitive Science, 2(1), 119–143. Google Scholar
  34. Londfors, A.-L. (2003). Tense and aspect in Swahil. Unpublished manuscript. Google Scholar
  35. MacWhinney, B. (2000). The CHILDES project: tools for analyzing talk. Hillsdale: Erlbaum. Google Scholar
  36. Meillet, A. (1909). Sur la disparition des formes simples du prétérit. In Linguistique historique et linguistique générale (pp. 149–158). Geneve/Paris: Slatkine/Champion. Google Scholar
  37. Mühlenbernd, R. (2011). Learning with neighbours. Synthese, 183(S1), 87–109. CrossRefGoogle Scholar
  38. Mühlenbernd, R. (2013). Signals and the structure of societies. Doctoral Thesis, University of Tübingen, TOBIAS-Lib Online Publication. Google Scholar
  39. Nettle, D. (1999). Using social impact theory to simulate language change. Lingua, 108(2–3), 95–117. CrossRefGoogle Scholar
  40. Page, K. M., & Nowak, M. A. (2002). Unifying evolutionary dynamics. Journal of theoretical biology, 219(1), 93–98. CrossRefGoogle Scholar
  41. Polomé, E. (1967). Swahili language handbook. Washington D.C.: Center for Applied Linguistics. Google Scholar
  42. Rosenbach, A. (2008). Language change as cultural evolution: Evolutionary approaches to language change. In R. Eckardt, G. Jäger, & T. Veenstra (Eds.), Variation, selection, development: probing the evolutionary model of language change (pp. 23–74). Berlin: de Gruyter. Google Scholar
  43. Roth, A. E., & Erev, I. (1995). Learning in extensive-form games: experimental data and simple dynamic models in the intermediate term. Games and Economic Behaviour, 8, 164–212. CrossRefGoogle Scholar
  44. Schaden, G. (2012). Modelling the ‘aoristic drift of the present perfect’ as inflation: an essay in historical pragmatics. International Review of Pragmatics, 4, 261–292. CrossRefGoogle Scholar
  45. Skyrms, B. (1996). Evolution of the social contract. Cambridge: Cambridge University Press. CrossRefGoogle Scholar
  46. Skyrms, B. (2010). Signals: evolution, learning, and information. London: Oxford University Press. CrossRefGoogle Scholar
  47. Smith, N. (2002). Ever moving on? The progressive in recent British English. In P. Peters, P. Collins, & A. Smith (Eds.), New frontiers in corpus research (pp. 317–330). Amsterdam: Rodopi. Google Scholar
  48. Taylor, P. D., & Jonker, L. B. (1978). Evolutionary stable strategies and game dynamics. Mathematical Biosciences, 40(1), 145–156. CrossRefGoogle Scholar
  49. Wärneryd, K. (1993). Cheap talk, coordination, and evolutionary stability. Games and Economic Behavior, 5, 532–546. CrossRefGoogle Scholar
  50. Williams, C. (2002). Non-progressive and progressive aspect in English. Fasano: Schena. Google Scholar
  51. Yanovich, I. (unpublished). Analysing imperfective games. Unpublished manuscript. Eberhard Karls Universität Tübingen. Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Eberhard Karls Universität TübingenTübingenGermany
  2. 2.Ludwig-Maximilians-Universität MünchenMunichGermany

Personalised recommendations