I've been thinking a lot about semantic meaning recently, especially in regard to Godel's Incompleteness Theorem. Anyway, I remain convinced that the meaning of a proposition is found in its method of verification or falsification. I believe that the meaning of a proposition to an individual is itself a theory about the methods of verification for that proposition. I say it is a theory because we generally cannot know with certainty the meaning of a given proposition (Quine's indeterminacy of translation). This is a subtle point because uncertainty in meaning can generally be rendered as small as necessary for any given task. It's only a major limitation when your theory of meaning cannot be verified, not even to yourself.
For example, if you tell me "the quijibo of 5 is 0.2", I will form a theory about the quijibo operator. It might mean an inversion, or it might mean multiplication by 0.04, or any of an infinite number of other possible operations. I will usually assume the simplest one I can think of (humans are simpletons for the most part). I can then evaluate the additional propositions you give me as tests of my quijibo theory.
So, if you give me a mathematical proposition, e.g., "the sum of the squares of 3 and 4 is equal to the square of 5", your proposition is meaningful because I have confidence that I know how to duplicate your computational experiment. I can square the numbers myself and come to the same conclusion (if I get my sums right). Of course, there are many pre-requisites, such as our mathematical axioms, but these can still be communicated sufficiently precisely for the proposition to make sense.
Likewise, propositions about the real world have meaning when a suitable physical experiment can be devised to test the proposition. The proposition need not be about an actual existent object, but the proposition makes sense if I can devise an experiment that would detect it if it did exist.
According to this model of semantic meaning, an AI can only understand a proposition if it can create a theory about what the proposition means, and knows how to perform the computational or physical tests needed to verify it.