They should not be followed up and continued. Isaac Asimoc(sic) died forty years after they were first written. If he had wanted to follow them up, he would have. The author’s intentions need to be respected here.Ok, I'll agree there's logic to that. I'm sure if Asimov had wanted to toss another robot book in there, he would have. It's not like he had any shortage of opportunity to publish new books, there's only a few hundred titles out there with his name on them.
However, can't we at least wait for the books to come out before we declare them a desecration? We've been down this path before, with both well-known (Bear, Benford, and Brin with the Second Foundation Trilogy) and lesser-known authors (Robot City). The Second Foundation Trilogy, while not Asimov books, were excellent in their own right, and Robot City was at least an acceptable read. (We won't discuss the movie; in fact, it's best to just pretend it never happened since it was never really intended to be related anyway.) Even though they're never "the same" as what came before, when a series is extended by a different author it can still result in excellent work–let's hold off on the pitchfork-and-torch brigade until we at least have something to look at.