Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence (IJCAI-19) Best Answers over Incomplete Data : Complexity and First-Order Rewritings Amelie´ Gheerbrant and Cristina Sirangelo Universite´ de Paris, IRIF, CNRS, F-75013 Paris, France famelie,
[email protected] Abstract as if nulls were usual data values, thus merely using the stan- dard database query engine to compute certain answers. Answering queries over incomplete data is ubiqui- In general though it is a common occurrence that few if tous in data management and in many AI applica- any certain answers can be found. If there are no certain an- tions that use query rewriting to take advantage of swers, it is still useful to provide a user with some answers, relational database technology. In these scenarios with suitable guarantees. To address this need, a framework one lacks full information on the data but queries to measure how close an answer is to certainty has recently still need to be answered with certainty. The cer- been proposed [Libkin, 2018b], setting the foundations to tainty aspect often makes query answering unfeasi- both a quantitative and a qualitative approach. We focus on ble except for restricted classes, such as unions of the qualitative notion of best answers. Those are a refinement conjunctive queries. In addition often there are no, of certain answers based on comparing query answers; one or very few, certain answers, thus expensive com- that is supported by a larger set of complete interpretations is putation is in vain. Therefore we study a relax- better. Best answers are those answers for which there is no ation of certain answers called best answers.