Resolving Complement Anaphora

In a quantified expression, the possibility of referring to the set-theoretical difference of restrictor and scope is known as complement anaphora (CA). Existing literature suggests two ways of analyzing this phenomenon either as confusion with reference to the maximal set, or as genuine complement reference. This paper will show that resolving an anaphor to the complement set is never a viable option. This will be motivated by adopting a formal semantic approach based on optimalitytheoretic constraints. Crucially, CA is licensed only by proportional right monotone decreasing determiners. Since proportional determiners introduce their restrictors into the discourse via an accommodated presupposition, the maximal set will always serve as a better candidate for anaphora resolution than the complement set. Further support of this conclusion stems from an independent maximality effect of CA, which follows naturally from the proposed analysis.