For as long as databases have existed, they have held themselves to an invariant. This invariant has become so ingrained into the psyche of database theoreticians, researchers, and designers that even the few who have tried to break it have only done so with cumbersome data models, by involving huge warning signs, or by using similarly obnoxious user interfaces. The invariant that I'm talking about is that a database must never give the user an incorrect answer.
Admittedly, this invariant has been broken now and again: Approximate (née. Online) Query Processing uses sampling to satisfy user-provided bounds, Probabilistic and Uncertain Databases work with underspecified data, while Model Databases allow users to query graphical models. Yet, even in these cases, we as a community feel compelled to force the user to suffer immeasurable pain and anguish for the sin of working with uncertain data. Probabilistic databases are impenetrable to anyone without a degree in statistics. Every single AQP system and model database adds arcane syntax to SQL that allows users to specify how much uncertainty they're willing to tolerate, or worse still, requires a magical frontend that screams at the top of its lungs about just how bad the results that it's producing are.