I am in respectful disagreement with this statement for the following reason. Much of the art from the medieval period of European art had an understanding that the symbolism contained within would be immediately identifiable by the viewer and this is something that is lost to most of us today. We may think we know the meaning of a piece, but can that be certain if we do not speak the language of its symbols? And if we can fit Medieval art (or any other symbolic art in history) within the definition of requiring specific cultural knowledge, then Postmodernism as an art movement seems not to be defined by this criterion.
hmm, that does seem to be a problem. I don't know anything about art history, but I can see that under my definition, most symbolic art falls under the category of 'post-modern'. Maybe the problem comes from the definition taking the term 'post-modern' literally, (ie: "it requires modern cultural knowledge, so it's post-modern").