Complement Anaphora and Interpretation

Quantificational sentences D(A)(B) allow for subsequent plural anaphoric reference to three sets associated with them: the maximal set A, the reference set A ∩ B and, sometimes, the complement set A ∩ - B. The latter case, where an anaphor refers to the set-theoretical difference of restrictor and scope, has been studied by both psycholinguists and formal semanticists. The phenomenon is particularly interesting because the conditions under which complement anaphora (as this case of anaphora is called) is acceptable depend on formal properties of the antecedent determiner. This paper concentrates on the interpretation of complement anaphora. First, the possibility of reducing complement anaphora to quasi-generic reference to the maximal set (A) is dismissed. Then, I argue that interpreting complement anaphora involves a conflict of several pragmatic constraints. A preliminary optimality theoretic analysis of the paradigm shows that if a strict principle disallowing empty complement set reference is obeyed, complement anaphora can overrule a general preference for reference to A∩B in order to save consistency. Finally, I argue that this non-emptiness condition ought to be reduced to inferability of the existence of a complement set. The contrast between pronominal complement anaphors and other pronouns that link to quantificational sentences is thus explained in terms of a contrast between pronouns with an inferred antecedent and pronouns that choose a salient antecedent.