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We show that the interpretation of sentences like John is not very Adj depends on whether Adj is vague. We argue that this follows from a constraint on the interaction between vagueness and conversational implicature, a domain that has not been studied extensively. The constraint states that implicatures are not drawn if they lead to "borderline contradictions" (see Ripley 2011 ; Alxatib & Pelletier 2011 ; a.o.), a natural extension of the idea that implicatures should not contradict assertions (Hackl 2006 ; Fox 2007 ; a.o.). Experiment 1 establishes that not very Adj gives rise to the implicature Adj for the non-vague absolute adjective late, but not for the vague relative adjective tall (in the terminology of Kennedy & McNally 2005a). Experiment 2 generalizes this result to three relative adjectives in the positive form (tall, hot, fast), against those same adjectives in their (non-vague) comparative forms (taller / hotter / faster than the average X). We also constructed quantitative meaning representations for complex predicates of the form Adj |$ \wedge \neg $| very Adj, using fuzzy logic to model the contribution of boolean connectives and our experimental data to represent the meanings of adjectives. The results of these analyses suggest that strengthening not very Adj with Adj leads to a more contradictory interpretation when Adj is vague than when it is not, as expected on our theory. While our results apply directly to only a specific set of lexical items, we hypothesize that they reflect a more general pattern among gradable predicates. This motivates more systematic investigation into the role that vagueness can play in the derivation of conversational implicatures. [ABSTRACT FROM AUTHOR]

What is the semantic content of a question? As pointed out by Karttunen (1977), declarative sentences that embed interrogative complements (such as 'John knows which students called') can provide relatively easy access to the semantics of questions. Recent theories attribute different readings to such sentences and their predictions depend in various ways on the embedding verb ('know' in this example). Through a series of four experiments, we provide quantitative offline data to evaluate critical judgments from the literature. We show that the so-called strongly exhaustive reading is not the only available reading for 'know', providing an argument against approaches inspired by Groenendijk & Stokhof (1982, 1984). We also describe processing data which may further constrain theories, provided hypotheses about the derivation processes are made explicit. [ABSTRACT FROM AUTHOR]