“[Potts] does not note that discourse anaphora from the CI content to the at-issue content seems entirely natural as shown by (4.24′) (a variant of his (4.24)), as does discourse anaphora from at-issue to CI content, illustrated by (4.76′) (a variant of his (4.76)):

(4.24′) Stan Bronowski, who took an exam, passed it with flying colors.

(4.76′) Several students, most of them linguists, missed the bus.

“By discourse anaphora, we mean here anaphora that does not involve binding, including but not limited to so-called E-type anaphora. We take it to be the same kind of anaphora that lends pronouns their intended interpretation cross-sententially, as in:

(4.24”) Stan Bronowski took an exam. He passed it with flying colors.

(4.76”) Several students missed the bus. Most of them were linguists.

Roberts (2004) argues that generalized quantifiers with existential entailments, like “several students”, can generally license discourse anaphora to the entailed entity, e.g. in (4.76′) and (4.76”) the set of students who missed the bus. Hence, it is not that “several students” either binds or is coreferential with “them”, but that its existential entailment makes weakly familiar a discourse referent, which latter satisfies the familiarity presupposition which her account posits for the pronoun.

“We can also construct such discourse anaphoric relations under a higher operator, as in (35), with anaphora from at-issue to CI content, and (36), with anaphora from CI to at-issue:

(35) Every professional man I polled said that while his wife, who had earned a bachelor’s degree, nevertheless had no work experience, he thought she could use it to get a good job if she needed one.

(36) In each class, several students failed the midterm exam, which they had to retake later.

We can naturally understand (36) to mean that there are both different students and different exams for each class, so that “several students” and “the midterm exam” have relational interpretations: ‘several students in x’ and ‘the midterm exam for x’ for some class x in the domain of each. Hence, the non-restrictive relative clause “which they had to retake later”—a supplemental CI in Potts’ terms—must take narrow scope under the universal each class, even though it is arguably speaker-oriented in the sense that the speaker is committed to its truth. The same is true of “who had earned a bachelor’s degree” in (35), by virtue of the fact that there are presumably different degrees for (the wives of) different professional men.”