Comparing exhaustivity operators

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Benjamin Spector


In this paper, I investigate the formal relationships between two types of exhaustivity operators that have been discussed in the literature, one based on minimal worlds/models, noted exh-mw (van Rooij & Schulz 2004, Schulz & van Rooij 2006, Spector 2003, 2006, with roots in Szabolcsi 1983, Groenendijk & Stokhof 1984), and one based on the notion of innocent exclusion, noted exh-ie (Fox 2007). Among others, I prove that whenever the set of alternatives relative to which exhaustification takes place is semantically closed under conjunction, the two operators are necessarily equivalent. Together with other results, this provides a method to simplify, in some cases, the computation associated with exh-ie, and, in particular, to drastically reduce the number of alternatives to be considered.

Besides their practical relevance, these results clarify the formal relationships between both types of operators.

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