Incomplete data: what went wrong, and how to fix it

Incomplete data is ubiquitous: the more data we accumulate and the more widespread tools for integrating and exchanging data become, the more instances of incompleteness we have. And yet the subject is poorly handled by both practice and theory. Many queries for which students get full marks in their undergraduate courses will not work correctly in the presence of incomplete data, but these ways of evaluating queries are cast in stone -- SQL standard. We have many theoretical results on handling incomplete data but they are, by and large, about showing high complexity bounds, and thus are often dismissed by practitioners. Even worse, we have a basic theoretical notion of what it means to answer queries over incomplete data, and yet this is not at all what practical systems do. Is there a way out of this predicament? Can we have a theory of incompleteness that will appeal to theoreticians and practitioners alike, by explaining incompleteness and being at the same time implementable and useful for applications? After giving a critique of both the practice and the theory of handling incompleteness in databases, the paper outlines a possible way out of this crisis. The key idea is to combine three hitherto used approaches to incompleteness: one based on certain answers and representation systems, one based on viewing incomplete databases as logical theories, and one based on orderings expressing relative value of information.