Identifying features in the presence of competing evidence.: The case of first-language acquisition

We discuss mathematical issues suggested by the processes of first-language acquisition and language change. We present a model of language acquisition with two components: A. probability measure describing sentence selection by a native speaker, and an identification principle modeling how the child chooses an element of the finite set of natural grammars. More generally we present an approach to the problem of classifying existing evidence to choose among a finite set of policies in the presence of possibly conflicting hints.