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		(a.1) M NaExb-identifies f (written: just in case for all a-noisy texts G for f, and  j M(G) =b f.

		(a.2) .

		(b.1) M InaExb-identifies f (written: just in case for all a-incomplete texts G for f, and  j M(G) =b f.

		(b.2) .

		(c.1) M ImaExb-identifies f (written: ) just in case for all a-imperfect texts G for f, and  j M(G) =b f.

		(c.2) .

		As an example of a collection of functions whose identifiability is not affected by the presence of a finite number of inaccuracies in texts, consider the class of constant functions, i.e., . It is easy to construct a scientist that identifies on *-noisy texts, *-incomplete texts, and *-imperfect texts. On the other hand, no scientist identifies , the collection of self-describing functions1, from 1-incomplete texts.

		The basic idea of the foregoing Definitions 8.6 and 8.9 is easily extended to other criteria of learning introduced in Chapter 6. For example, consider the language learning criterion , according to which a scientist M is successful on a language L just in case, given any text for L, M converges to a finite set of indexes D such that and each index in D is for some b-variant of L. An a-noisy-text version of is defined by requiring the scientist to a language on any a-noisy text. The resulting paradigm is named . With this background, the reader may easily formulate the exact definitions of the following paradigms for language identification: , , , NaTxtBcb, InaTxtBcb, and ImaTxtBcb.

		Several criteria of function identification studied in Chapter 6 may also be adapted to the present context. In particular, we shall focus on NaBcb, InaBcb, and ImaBcb in what follows.

		§8.1.2 Hierarchy Results

		The present section considers the tradeoff between inaccuracy in the available data versus leniency in the learning criterion. In particular, we investigate the effect of allowing

		1Recall from Chapter 4 (Definition 4.24) that .