A mathematical model of prediction-driven instability: how social structure can drive language change. (English) Zbl 1243.91095
Summary: I discuss a stochastic model of language learning and change. During a syntactic change, each speaker makes use of constructions from two different idealized grammars at variable rates. The model incorporates regularization in that speakers have a slight preference for using the dominant idealized grammar. It also includes incrementation: The population is divided into two interacting generations. Children can detect correlations between age and speech. They then predict where the population’s language is moving and speak according to that prediction, which represents a social force encouraging children not to sound out-dated. Both regularization and incrementation turn out to be necessary for spontaneous language change to occur on a reasonable time scale and run to completion monotonically. Chance correlation between age and speech may be amplified by these social forces, eventually leading to a syntactic change through prediction-driven instability.
MSC:
| 91F20 | Linguistics |
Keywords:
language variation; language change; incrementation; mathematical model; social structure; prediction-driven instabilityReferences:
| [1] | Adger D. (2003) Core syntax: A minimalist approach. Oxford University Press, Oxford |
| [2] | Bresnan, J., & Nikitina, T. (2007). The gradience of the dative alternation. In L. Uyechi, & L. H. Wee (Eds.), Reality exploration and discovery: Pattern interaction in language and life. Stanford: CSLI Publiscations. http://www.stanford.edu/\(\sim\)bresnan/publications/index.html . |
| [3] | Briscoe E. J. (2000) Grammatical acquisition: Inductive bias and coevolution of language and the language acquisition device. Language 76(2): 245–296 |
| [4] | Briscoe, E. J. (2002). Grammatical acquisition and linguistic selection. In E. J. Briscoe (Ed.), Linguistic evolution through language acquisition: Formal and computational models. Cambridge: Cambridge University Press. http://www.cl.cam.ac.uk/users/ejb/creo-evol.ps.gz . |
| [5] | Ellegård A. (1953) The auxiliary do: The establishment and regulation of its use in English, Gothenburg studies in English. Almqvist and Wiksell, Stockholm |
| [6] | Gibson E., Wexler K. (1994) Triggers. Linguistic Inquiry 25: 407–454 |
| [7] | Gold E. M. (1967) Language identification in the limit. Information and Control 10: 447–474 · Zbl 0259.68032 · doi:10.1016/S0019-9958(67)91165-5 |
| [8] | Hudson Kam C. L., Newport E. L. (2005) Regularizing unpredictable variation: The roles of adult and child learners in language formation and change. Language Learning and Development 1(2): 151–195 · doi:10.1207/s15473341lld0102_3 |
| [9] | Kirby S. (2001) Spontaneous evolution of linguistic structure: An iterated learning model of the emergence of regularity and irregularity. IEEE Transactions on Evolutionary Computation 5(2): 102–110 · doi:10.1109/4235.918430 |
| [10] | Komarova N. L., Niyogi P., Nowak M. A. (2001) The evolutionary dynamics of grammar acquisition. Journal of Theoretical Biology 209(1): 43–59 · doi:10.1006/jtbi.2000.2240 |
| [11] | Kroch A. (1989) Reflexes of grammar in patterns of language change. Language Variation and Change 1: 199–244 · doi:10.1017/S0954394500000168 |
| [12] | Labov W. (1994) Principles of linguistic change: Internal factors. Blackwell, Cambridge, MA |
| [13] | Labov W. (2001) Principles of linguistic change: Social factors. Blackwell, Cambridge, MA |
| [14] | Mitchener W. G. (2003) Bifurcation analysis of the fully symmetric language dynamical equation. Journal of Mathematical Biology 46: 265–285. doi: 10.1007/s00285-002-0172-8 · Zbl 1081.91026 · doi:10.1007/s00285-002-0172-8 |
| [15] | Mitchener W. G. (2007) Game dynamics with learning and evolution of universal grammar. Bulletin of Mathematical Biology 69(3): 1093–1118. doi: 10.1007/s11538-006-9165-x · Zbl 1298.92073 · doi:10.1007/s11538-006-9165-x |
| [16] | Mitchener, W. G. (2009a). Mean-field and measure-valued differential equation models for language variation and change in a spatially distributed population, submitted. · Zbl 1221.34129 |
| [17] | Mitchener, W. G. (2009b). A stochastic model of language change through social structure and prediction-driven instability, submitted. · Zbl 1384.37115 |
| [18] | Mitchener W. G., Nowak M. A. (2003) Competitive exclusion and coexistence of universal grammars. Bulletin of Mathematical Biology 65(1): 67–93. doi: 10.1006/bulm.2002.0322 · Zbl 1334.91065 · doi:10.1006/bulm.2002.0322 |
| [19] | Mitchener W. G., Nowak M. A. (2004) Chaos and language. Proceedings of the Royal Society of London, Biological Sciences 271(1540): 701–704. doi: 10.1098/rspb.2003.2643 · doi:10.1098/rspb.2003.2643 |
| [20] | Niyogi P. (1998) The informational complexity of learning. Kluwer Academic Publishers, Boston · Zbl 0976.68125 |
| [21] | Niyogi P., Berwick R. C. (1996) A language learning model for finite parameter spaces. Cognition 61: 161–193 · doi:10.1016/S0010-0277(96)00718-4 |
| [22] | Niyogi, P., & Berwick, R. C. (1997). A dynamical systems model for language change. Complex Systems, 11, 161–204, ftp://publications.ai.mit.edu/ai-publications/1500-1999/AIM-1515.ps.Z . |
| [23] | Nowak M. A., Komarova N. L., Niyogi P. (2001) Evolution of universal grammar. Science 291(5501): 114–118 · Zbl 1226.91060 · doi:10.1126/science.291.5501.114 |
| [24] | Nowak M. A., Komarova N. L., Niyogi P. (2002) Computational and evolutionary aspects of language. Nature 417(6889): 611–617 · doi:10.1038/nature00771 |
| [25] | Radford A. (2004) Minimalist syntax: Exploring the structure of English. Cambridge University Press, Cambridge |
| [26] | Tesar B., Smolensky P. (2000) Learnability in optimality theory. MIT Press, Cambridge, MA |
| [27] | Warner A. (2005) Why DO dove: Evidence for register variation in early modern English negatives. Language Variation and Change 17: 257–280. doi: 10.1017/S0954394505050106 · doi:10.1017/S0954394505050106 |
| [28] | Yang C. D. (2002) Knowledge and learning in natural language. Oxford University Press, Oxford |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
