In two experiments, we study the effects of verb concepts on the interpretation of reciprocal expressions in Dutch and Hebrew. One experiment studies Hebrew to test a previous account, the Strongest Meaning Hypothesis, which suggests that listeners resolve ambiguity in reciprocal sentences using the logically strongest meaning that is consistent with the context. The results challenge this proposal, as participants often adopt a weaker meaning than what the Strongest Meaning Hypothesis expects. We propose that these results reflect the sensitivity of reciprocal quantifiers to verb concepts, which is modelled by a new principle, the Maximal Typicality Hypothesis (MTH). For any given reciprocal sentence, the MTH specifies a core situation: the maximal situation that is also maximally typical for the verb concept. The MTH predicts reciprocal sentences to be maximally acceptable in the core situation and, under certain conditions, in situations that contain it, but substantially less acceptable in other situations. To test this prediction, we conducted a two-part experiment among Dutch speakers: (a) a membership test that ranks typicality preferences with different verbs; (b) a truth-value judgement test with reciprocal sentences containing these verbs. The results show that the typical number of patients per agent varies between verbs, with a significant effect of these preferences on reciprocal quantification: the stronger the verb concept's bias is for one-patient situations, the weaker is the interpretation of reciprocal sentences containing it. These results support the MTH as a basis for a general theory of reciprocal quantification.

A basic puzzle about presuppositions concerns their projection from propositional constructions. This problem has regained much attention in the last decade since many of its prominent accounts, including variants of the trivalent Strong Kleene connectives, suffer from the so-called *proviso problem*.This paper argues that basic insights of the Strong Kleene system can be used without invoking the proviso problem. It is shown that the notion of *determinant value* that underlies the definition of the Strong Kleene connectives leads to a natural generalization of the filtering conditions proposed in Karttunen's article ``Presuppositions of compound sentences'' (LI, 1973). Incorporating this generalized  condition into an incremental projection algorithm avoids the proviso problem as well as the derivation of conditional presuppositions. It is argued that the same effects that were previously modelled using conditional presuppositions may be viewed as effects of presupposition suspension and contextual inference on presupposition projection.

In binary propositional constructions S 1 con S 2 , the Strong Kleene connectives explain filtering of S 1 's and S 2 's presuppositions depending on their logical relations with their non-presuppositional content. However, the presuppositions derived by the Strong Kleene connectives are weak conditional presuppositions, which raise the "proviso problem" in cases where no filtering is motivated. Weak Kleene connectives do not face this problem, but only because their presuppositions are often too strong, and hence do not account for filtering phenomena altogether. While various mechanisms have been proposed to allow filtering without the proviso problem, their relations with the standard trivalent Kleene systems have remained unclear. This paper shows that by sacrificing truth-functionality, we uncover a rich domain of possibilities in trivalent semantics in between the Weak Kleene and Strong Kleene connectives. These systems derive presupposition filtering while avoiding the proviso problem. The Kleene-style operators studied are generalized to arbitrary binary functions, which further clarifies the connection between their different "repair" strategies and presupposition projection.