When it comes to the copula sentence, usually the noun phrase preceding the copula is subject.
(1)The problem is the kids. (2)??The problem are the kids. (3)The kids are the problem. (4)*The kids is the problem.
My question is what the differences are between (1) and (3)? Do they mean the same? What is the inner reason for such minor differences? And for equational sentences, (a subset of copular sentences), how could we draw the trees building on the framework of phrase structure grammar?
As Tim has pointed out,
"The aspect of the question that makes it appropriate for this forum is the fact that to answer it well, one should consider how such sentences are produced in other languages. In German, for instance, sentence (2) would have agreement with the post-copular NP, i.e. Das Problem sind /*ist die Kinder. Furthermore, the basic issue concerns the distinction between specificational and predicational copular sentences, areas that are of relevance to theoretical syntax. "
Thanks, @Tim for helping me clarify the questions.
Update: here is an interesting video considering this: https://www.youtube.com/watch?v=EjEi7T8hYmY