Introduction:
Two experiments presented infants with artificial languages in which at least two generalizations were logically possible. The results demonstrate that infants made one of the two generalizations tested, the one which was most statistically consistent with the particular subset of the data they received.
I will focus on the induction problem - the situation in which a subset of input clearly has at least two formal descriptions. What does an infant learner exposed to such input do? There are at least three possibilities: One is that the infant discerns both patterns embodied in the input and can generalize based on either one. A second possibility is that being faced with evidence of two possible generalizations prevents the learner from generalizing at all. Finally, and perhaps most interestingly, the infant might show evidence of having discerned different formal descriptions for different subsets of the input, depending on which description better accounts for that particular input.
Infants in the diagonal condition were familiarized with a subset of the stimuli in which the only common feature was an abstract AAB or ABA pattern. Like the infants studied by Marcus et al. (1999), infants in this condition were able to generalize to new test stimuli, suggesting that they had made the intended generalization, having only been exposed to four stimulus types. Infants in the column condition, who were exposed to a different subset of the same larger data set, failed to make the generalization. This pattern of results is consistent with two possible interpretations: Infants exposed to input consistent with two different formal systems make no generalization at all. Or, infants generalize based on the formal description that is more likely to have generated the input.
These data, coupled with infants’ failure to discriminate under the same familiarization conditions in Exp. 1, suggest that infants in the column condition made only the generalization involving the position of the syllable di.
A question raised by the experiments is what caused infants in the column condition to generalize based on the location of di rather than making the more abstract generalization?
One possibility is that the data are consistent with the Subset Principle (Manzini & Wexler, 1987), in which learners select among possible parameter values based on which value generates the smallest language compatible with the input data. Note that, if we interpret ‘language’ to mean ‘set of sentences,’ a learner would need to generate all of the sentences for each parameter value and determine which value generated fewer sentences (but see Wexler, 1993). Wexler and Manzini reduce the computational task for the learner by placing relevant parameters in a markedness hierarchy, in which the learner begins with the least marked value, which generates the smallest language.
Another possibility is consistent with the Bayesian approaches to generalization (e.g., Tenenbaum & Griffiths, 2001), in which learners compare the subset of the input they have received to the range of input generated by different formal descriptions. For example, an infant might tacitly compute that it is extremely unlikely, given an AAB grammar, the only input ends in di. Depending on its implementation, this approach might also be computationally challenging. However, it has the advantage of applying to a more general (e.g., non-parameterized) learning problems, and it allows increasing confidence in hypothesis selection with increasing input set size. Importantly, this solution to the induction problem entails learners choosing among formal descriptions that they have already generated from the data using general purpose mechanisms (Saffran, Reeck, Niebuhr, & Wilson, 2005) or that are part of their innate endowment for language (e.g. Valian, 1990). For example, Saffran et al. (2005) demonstrated that the structure of the input determines the primitives (in this case absolute vs. relative pitch) over which generalizations are made. This type of research, in which learners ‘choose’ among different generalizations allowed by input data, may ultimately allow us to distinguish between theories of language development.