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If the text T indicated in 3.3 continues by listing all the odd numbers, then Fperiods, of 3.8 identifies T. In contrast, if T is for any set other than P, O, or N, then Fperiods does not identify T. For other examples, let Ffinite and Ffive, be as specified in 3.9. Ffinite> identifies any text for a finite language and no text for an infinite one. Ffive identifies a given text T if and only if content(T) = W5. |
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§3.4.2 Identifying Languages |
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Children are able to learn a language on the basis of many orderings of its sentences. Since Definition 3.10 pertains to individual texts, it does not represent this feature of language acquisition. Similarly, our scientist studying periods might converge to a correct grammar for the set, regardless of the way Nature lists it for her. The next definition incorporates this feature of empirical inquiry. |
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3.11 Definition (Gold [80]) |
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Let scientist F and  be given. F identifies L just in case F identifies every text for L. |
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It is easy to verify that Fperiods identifies P, O, and N. Ffinite identifies every finite language but no infinite one. Ffive identifies W5 and nothing else. |
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Suppose that scientist F identifies language L, and let T and T' be different texts for L. It is consistent with Definition 3.11 that F converge on T and T' to different grammars for L. Likewise, F might require more inputs from T than from T' before emitting a grammar for L. |
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§3.4.3 Identification of a Collection of Languages |
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Children are able to learn any arbitrarily selected language drawn from a large class; that is, their acquisition mechanism is not prewired for just a single language. Similarly, there might be a wide subcollection  of e such that our scientist studying periods would succeed on any text for any member of  . Our definition of identification is now extended accordingly. |
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3.12 Definition (Gold [80]) Let scientist F and  be given. F identifies  just in case F identifies each  .  is said to be identifiable just in case some scientist identifies it; it is said to be unidentifiable otherwise. |
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We use  to represent collections of languages. The following reformulation of Definition 3.12 is worth recording. |
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