Comparing Exhaustivity Operators (minimal worlds vs. innocent exclusion)
Benjamin Spector

 

Spector, Benjamin. 2016. Comparing exhaustivity operators. Semantics and Pragmatics 9(11). http://dx.doi.org/10.3765/sp.9.11.

 

Abstract:

 

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 (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 (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 innocent exclusion, 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.