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Disjunction in alternative semantics
The standard semantic analysis of natural language disjunction maintains that or is the Boolean join. This dissertation makes a case for a Hamblin-style semantics, under which disjunctions denote sets of propositions. ^ Chapter 2 shows that the standard semantics does not capture the natural interpretation of counterfactual conditionals with disjunctive antecedents. Together with a standard minimal change semantics for counterfactuals, the standard semantics predicts that these counterfactuals are evaluated by selecting the closest worlds from the union of the propositions that or operates over. Their natural interpretation, however, requires selecting the closest worlds from each of the propositions that or operates over. This interpretation is predicted under a Hamblin-style semantics if conditionals are analyzed as correlative constructions. ^ Chapter 3 deals with the exclusive component of unembedded disjunctions. The exclusive component of a disjunction S with more than two atomic disjuncts can be derived as an implicature if S competes in the pragmatics with all the conjunctions that can be formed out of its atomic disjuncts. The generation of these pragmatic competitors proves challenging under the standard analysis of or, because the interpretation system does not have access to the atomic disjuncts. Under a Hamblin semantics, however, the required pragmatic competitors can be generated by mapping each non-empty subset B of the denotation of S to the proposition that is true in a world w if and only if all the members of B are true in w. ^ Chapter 4 investigates the interpretation of disjunctions under the scope of modals. When uttered by a speaker who knows who may have what, a sentence of the form of Sandy may have ice cream or cake naturally conveys that Sandy has two rights: the right to have ice cream, and the right to have cake. Under the standard analysis of or and modals, however, the sentence is predicted to be true as long as Sandy has at least one of the rights. A Hamblin style analysis allows for the derivation of the requirement that Sandy has two rights as an implicature of domain widening. ^
Alonso-Ovalle, Luis, "Disjunction in alternative semantics" (2006). Doctoral Dissertations Available from Proquest. AAI3242324.