Saul Kripke, in his paper "An Outline of a Theory of Truth", talks a little about sentences that don't receive determinate truth values in virtue of their logical structure, such as the self-referential examples you're talking about. Kripke calls these "Ungrounded" sentences. The general intuition behind the idea of ungroundedness is that the valuation of some sentences might be totally unsettled by the way the world is taken to be, and that this shouldn't stop us being able to account for a theory of those sentences that do receive a determinate and positive truth value.
On the face of it, "Every kind of berry is something that Alice likes" doesn't appear to be ungrounded in Kripke's sense. If a "kind of berry" is something that Alice can have an attitude towards, and Alice has a positive attitude towards every such kind of berry, then the sentence works out true, and otherwise, it works out false. Now we can reasonably discuss the possibility that neither kinds of berries nor the attitude of liking are usefully described with the particular logical structure that underlies the standard modelling view I've supposed here, but then we need to ask more about what it is you mean when you're talking about berries and liking.
But! There may well be other sentences that work out as ungrounded that aren't purely self-referential. Consider the following example Kripke gives. Richard Nixon is well known for having told a lot of lies about his involvement in the Watergate affair. So suppose that someone, named Jones, who has otherwise nothing to say about the scandal, claims of Nixon that:
All of the claims made by Nixon about Watergate are false.
Let's also suppose that Nixon knows Jones personally, and, generally thinking that Jones will be supportive of him, asserts that:
Everything that Jones says about Watergate is true.
Both of these sentences have meanings such that we know where we would need to go and look, independently, in order to determine whether they came out true or false. However, since it turns out that they are in fact mutually dependent on one another for their truth value, it will turn out that they are both Ungrounded sentences when we theorise about them in a Kripkean theory of assigning truth values.