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§8.2.2 Informant Presentation |
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It is often assumed that children do not receive direct information about the non-sentences of their language (see the discussion in Chapters 1 and 3). Let us consider, however, what happens when texts contain both positive and negative information. |
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8.30 Definition We say that a text G for a 0-1 valued function is an informant for L just in case  . |
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8.31 Definition Let  . |
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(a) A scientist M InfTxtExa-identifies L (written:  ) just in case on all informants G for L,  and WM(G) =a L. |
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(b)  . |
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We can similarly define M InfTxtBca, etc. It is easy to see that  and  . We now prove the following Proposition which shows the distinction between the two. |
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8.32 Proposition  . |
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Proof: Let  . It is easy to see that  , but not in AscTxtBc*. |
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§8.2.3 Recursive Texts and Nonrecursive Texts |
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A text, T, is said to be recursive just in case them exists a recursive function f such that for all n, f(n) = T(n). |
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If children s caretakers are machine simulable and are sheltered from random environmental influence, they might be limited to the production of recursive texts. Similarly, if natural phenomena are computable processes devoid of any random behavior, a scientist may be restricted to operating on recursive texts. Would such a limitation affect in principle the class of learnable languages? We first incorporate the notion of recursive texts into our learning paradigm. |
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8.33 Definition Let  . |
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(a) M RecTxtExa-identifies L (written :  ) just in case for all recursive texts T for L,  and WM(T) =a L |
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