Given two propositions, each separately acceptable, must their conjunction be acceptable as well? Systems of non-monotonic reasoning generally say "yes", whereas a naive use of probabilities suggests "no" (sidestepping the so-called Lottery Paradox). Both answers will be investigated in a minimal "qualitative" setting given by Keisler's weak logic for generalized quantifiers. The notion of a filter will be weakened to capture families of sets with probability above some threshold (relative to some fixed measure). Applications to natural language will be discussed.

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