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Fronting a noun phrase changes the focus structure of a sentence. Therefore, it may affect truth conditions, since some operators, in particular quantificational adverbs, are sensitive to focus. However, the position of the quantificational adverb itself, hence its informational status, is usually assumed not to have any semantic effect. In this paper I discuss a reading of some quantificational adverbs, the relative reading, which disappears if the adverb is fronted. I propose that this reading relies not only on focus, but on B-accent (fall-rise intonation) as well. A fronted Q-adverb is usually pronounced with a B-accent; since only one element can be B-accented, this means that the scope of the adverb contains no B-accented material, hence no relative readings. Thus, the effects of fronting range more widely than is usually assumed, and quantificational adverbs are a useful tool with which to investigate these effects.
In this paper I discuss four type of bare nominal, and note that, in some sense, all of them appear to imply stereotypicality. I consider an account in terms of Bidirectional Optimality Theory: unmarked (bare) forms give rise to unmarked (stereotypical) interpretations. However, it turns out that, while the form of bare numerals is unmarked, the interpretation sometimes is not. I suggest that the crucial notion is not unmarkedness, but optimal inference: unmarked forms give rise to interpretations that are best used for drawing inferences. I propose a revision of Bidirectional Optimality Theory to reflect this.