Combining Data and Mathematical Models of Language Change

Proceedings of the 48th Annual Meeting of the Association for Computational Linguistics, pages 1019–1029, Uppsala, Sweden, 11-16 July 2010. c⃝2010 Association for Computational Linguistics Combining data and mathematical models of language change Morgan Sonderegger University of Chicago Chicago, IL, USA. morgan@cs.uchicago.edu Partha Niyogi University of Chicago Chicago, IL, USA. niyogi@cs.uchicago.edu Abstract English noun/verb (N/V) pairs (contract, cement) have undergone complex patterns of change between 3 stress patterns for several centuries. We describe a longitu- dinal dataset of N/V pair pronunciations, leading to a set of properties to be ac- counted for by any computational model. We analyze the dynamics of 5 dynamical systems models of linguistic populations, each derived from a model of learning by individuals. We compare each model’s dy- namics to a set of properties observed in the N/V data, and reason about how as- sumptions about individual learning affect population-level dynamics. 1 Introduction The fascinating phenomena of language evolution and language change have inspired much work from computational perspectives in recent years. Research in this field considers populations of lin- guistic agents, and asks how the population dy- namics are related to the behavior of individual agents. However, most such work makes little contact with empirical data (de Boer and Zuidema, 2009).1 As pointed out by Choudhury (2007), most computational work on language change deals with data from cases of change either not at all, or at a relatively high level.2 Recent computational work has addressed “real world” data from change in several languages (Mitchener, 2005; Choudhury et al., 2006; Choud- hury et al., 2007; Pearl and Weinberg, 2007; Da- land et al., 2007; Landsbergen, 2009). In the same 1However, among language evolution researchers there has been significant recent interest in behavioral experiments, using the “iterated learning” paradigm (Griffiths and Kalish, 2007; Kalish et al., 2007; Kirby et al., 2008). 2We do not review the literature on computational studies of change due to space constraints; see (Baker, 2008; Wang et al., 2005; Niyogi, 2006) for reviews. spirit, we use data from an ongoing stress shift in English noun/verb (N/V) pairs. Because stress has been listed in dictionaries for several centuries, we are able to trace stress longitudinally and at the level of individual words, and observe dynam- ics significantly more complicated than in changes previously considered in the computational litera- ture. In §2, we summarize aspects of the dynamics to be accounted for by any computational model of the stress shift. We also discuss proposed sources of these dynamics from the literature, based on ex- perimental work by psychologists and linguists. In §3–4, we develop models in the mathemati- cal framework of dynamical systems (DS), which over the past 15 years has been used to model the interaction between language learning and lan- guage change in a variety of settings (Niyogi and Berwick, 1995; Niyogi and Berwick, 1996; Niyogi, 2006; Komarova et al., 2001; Yang, 2001; Yang, 2002; Mitchener, 2005; Pearl and Weinberg, 2007). We interpret 6 aspects of the N/V stress dy- namics in DS terms; …

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