A central question in the study of presuppositions is how a presupposition trigger contributes to the meaning of a complex expression containing it. Two competing answers are found in the literature on quantificational expressions. According to the first, a quantificational expression presupposes that every member of its domain satisfies the presuppositions triggered in its scope, and according to the second, a quantificational expression presupposes that at least one member of its domain satisfies the presuppositions triggered in its scope. The former view implies that an interrogative clause, a kind of quantificational expression, presupposes all of its possible answers’ presuppositions, whereas the latter view implies that an interrogative clause presupposes that the presuppositions of at least one of is possible answers are satisfied. This paper contributes to the debate by showing that ‘alternative’ interrogatives, formed with or, project presuppositions in the same, distinctive manner that other disjunctive constructions do: generally, universally. A theory that treats disjunctive words as restricted variables, bindable by various quantificational operators, is extended to account for the presuppositions of ‘alternative’ interrogatives, disjoined declaratives, and disjoined conditional antecedents in a uniform manner. The paper then explores some ways to reconcile the proposal with two special cases where interrogatives have been claimed to have weaker presuppositions: (1) constituent interrogatives in presupposition-weakening contexts, and (2) polar interrogatives containing bias-inducing scalar particles like even.

在前提研究中的一个中心问题是，前提触发是如何促进包含它的复杂表达式的含义的。在关于定量表达的文献中发现了两个相互竞争的答案。根据第一个，定量表达式的前提是其域的每个成员都满足在其范围内触发的前提；根据第二个，量化表达式的前提是，其域的至少一个成员都满足在其范围内触发的前提。前一种观点暗示一种疑问句，一种量化表达，以其所有可能答案的前提为前提，而后一种观点暗示一种疑问句，以至少一个可能答案的前提得到满足。或，以与其他析取结构相同，独特的方式投射预设：通常是普遍的。一种将析取词视为受限制变量的理论，可以被各种量化算符约束，这一理论被扩展为以统一的方式解释“另类”疑问词，不连贯的陈述式和不连贯的条件先决词的前提。然后，本文探索了一些方法来使提案与两种特殊情况相吻合，在两种特殊情况下，疑问句被认为具有较弱的前提条件：（1）在前提条件减弱的情况下构成疑问句，以及（2）包含偏倚诱导标量粒子（如even）的极性疑问句。