A: Morning.(I heard this said on TV; perhaps on Last of the summer wine.)
B: Glad you think so.
There is so much pragmatic implicature in here it's outrageous. B, by saying glad you think so (with stress on you), implies that he does not agree. But what is it that he does not agree with? Morning is not something you can agree or disagree with; it's not a proposition and as such has no propositional content and no truth-value. And it can't be interpreted as meaning that 'morning is here', or 'it is morning' - that's definitely not what he's disagreeing with.
Obviously, Morning is a truncated form of the greeting Good morning. The good is understood. This kind of shortening is something we do a lot, because it's a set phrase, said often, and we know what's meant even if half of it is missing. But in itself, this is not something you can (dis)agree with either: good morning is also not a proposition.
What we really mean when we say Good morning (or Morning) is I wish a good morning to you. We are expressing our hope that our interlocutor has a pleasant day. But again, you can't disagree with what someone hopes - it really isn't your place to do so.
B, in the exchange above, has correctly inserted the implicit Good, but then wilfully misinterpreted Good morning to be a shortened form of It is a good morning. That is a proposition, and can certainly have a truth value - it is either true that it is a good morning, or it is false.
If English still had a case system, incidentally, this kind of deliberate reanalysis couldn't happen. The phrase Good morning would be accusative in the speaker's intended interpretation, but nominative in the hearer's reanalysis. So presumably those languages that do have overt case lack this kind of hilarious repartee.