Abstract
In general, all human beings can learn any human language in their first language acquisition. One of the functions of language use is to communicate with others. In the work described here we investigate situations in which learners are exposed to more than one language. Our study leads us to suggest how creole languages could emerge. We make the assumption that the language learners come to acquire one of the languages that is optimal for communication, which would vary according to the environment. It is postulated that the most preferable language in the community would eventually survive and become dominant in competition with other languages, depending on how large a proportion of the people speak it. Accordingly, language change can be represented by population dynamics, examples of which include an agent-based model of language acquisition proposed by Briscoe et al. (2002) and a mathematical framework by Nowak et al. (2001), who elegantly presented an evolutionary dynamics of grammar acquisition in a differential equation, called the language dynamics equation.
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- 1.
In this chapter we take a grammar as equivalent to a language.
- 2.
A T denotes the transposed matrix of A.
- 3.
If the memoryless learner is able to choose the refused grammar again with a uniform probability when he failed to accept the sentence, the Markov matrix is replaced by:
$$M = \left( \begin{array}{ccc} 1 && 0\\ (1-a)/2 && a+(1-a)/2 \end{array} \right).$$ - 4.
For example, suppose there are two grammars, G 1 and G 2, and the number of input sentences is w = 1. Then, the learning accuracy of G 1 is \(q_{11} = 1-a/2-\alpha (1-a)(1-x_1+x_2)/2\), while \(q_{22} = 1-a/2-\alpha (1-a)(1+x_1-x_2)/2\) for G 2. When \(\alpha=0\), \(q_{11}=q_{22}\).
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© 2007 Springer-Verlag London Limited
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Nakamura, M., Hashimoto, T., Tojo, S. (2007). Language Change among ‘Memoryless Learners’ Simulated in Language Dynamics Equations. In: Lyon, C., Nehaniv, C.L., Cangelosi, A. (eds) Emergence of Communication and Language. Springer, London. https://doi.org/10.1007/978-1-84628-779-4_12
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DOI: https://doi.org/10.1007/978-1-84628-779-4_12
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