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		monotonicity. (See Exercise 5-19.) For this reason, in the next definition we introduce only the class version of monotonicity and, in keeping with the usage in the literature, refer to the class as [TxtEx]monotonic instead of [TxtEx]class-monotonic.

		5.51 Definition .

		The third generalization strategy, referred to as weak monotonic, allows a scientist to expel elements from its hypothesis only if it encounters elements in its evidential state that cannot be accounted for by its current hypothesis. More precisely:

		5.52 Definition (Lange and Zeugmann [119])

		(a) M is said to be weak monotonic on L just in case, for each with and each with we have that .

		(b) M is said to be weak monotonic on just in case M is weak monotonic on each .

		(c) M is weak monotonic just in case M is weak monotonic on each .

		So, if a weak-monotonic scientist conjectures index j after index i and the set of elements seen by the scientist when index j is conjectured is a subset of Wi, then . The collections of languages identified by the global and the class versions of weak-monotonic scientists are introduced in the next definition.

		5.53 Definition

		(a)

		(b) .

		It is easy to see that

		Equality follows using the following fact. (See Exercise 5-21.)

		We note that there is a similarity between weak-monotonicity and conservativeness. A conservative scientist can only change her hypothesis if the current hypothesis does not