Presupposition filtering in disjunction: The role of exclusive interpretation

Abstract

Kalomoiros and Schwarz (2024) report symmetric presupposition projection across disjunction, a key datum for theories of projection. This study further asks whether projection across disjunctions is affected by exclusive interpretations. We observe that many fully semantic implementations of exclusivity and presupposition projection converge on the same, previously untested prediction: exclusive disjunction yields uniform projection (i.e., no filtering for either disjunct), so increasing exclusivity should reduce filtering. Mayr and Romoli (2016a) derive this prediction for Strong Kleene semantics when exclusivity is computed via bivalent exhaustification, and we show that it also follows, under the same assumption, for George’s (2008) algorithm, and for dynamic semantics (Rothschild, 2011). We also derive this prediction for strong-negation variants of trivalent exhaustification (Spector and Sudo, 2017). We then test this prediction in a Mandarin acceptability-judgment experiment adapted from Kalomoiros and Schwarz (2024), manipulating the rate of exclusive readings via environmental monotonicity. In fact, we find no evidence that increasing exclusivity affects filtering. If this null effect proves robust, it puts pressure on most of the above semantic implementations and appears compatible with only a weak-negation version of trivalent exhaustification that has been argued to be undesirable for independent reasons (Spector and Sudo, 2017), so we discuss possible future paths.