Disjunctions in the scope of a possibility modal trigger so-called free choice inferences: (1a) gives rise to the inference (1b) (e.g., Kamp 1973).

In the literature, such inferences are typically (but not always) derived as implicatures, crucially relying on the assumption that a sentence with a disjunction activates domain alternatives. To understand what domain alternatives are, note that a disjunction can be described by the set of elements (objects or propositions) that it covers. For the disjunction in (1a), that set of elements, which we will refer to as the domain D of disjunction, would be D = {Article 1, Article 2, Article 3}. Domain alternatives of a disjunction are other disjunctions that differ from the original in that they are constructed on smaller domains D′⊆D. In other words, a sentence with a disjunction, schematically P(A1 or A2 or...

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