That would be the "small set of closed relations" case I'd mentioned above. The system of two statements is self-referential, in that it references nothing out

That would be the "small set of closed relations" case I'd mentioned above. The system of two statements is self-referential, in that it references nothing outside itself, that is, it only concerns what Allen (presuming "Alen" is a typo) and Bob say, but no other larger-world context. A somewhat trivial and contrived counterexample might be: Allen: What Bob is about to say is true and water is wet. Bob: What Allen just said is false and water is not wet. Here, we'd have to consider the truth values of both assertions, whether or not what the other party said is true, and whether or not water is wet. Both assertions would have to be true for the full statement to be true, either assertion being false would falsify the combined statement. And it is possible that both statements are false.