A Hybrid Approach to Answering Why-Not Questions on Relational Query Results

In analyzing and debugging data transformations, or more specifically relational queries, a subproblem is to understand why some data are not part of the query result. This problem has recently been addressed from different perspectives for various fragments of relational queries. The different perspectives yield different yet complementary explanations of such missing answers. This article first aims at unifying the different approaches by defining a new type of explanation, called hybrid explanation, that encompasses the variety of previously defined types of explanations. This solution goes beyond simply forming the union of explanations produced by different algorithms and is shown to be able to explain a larger set of missing answers. Second, we present Conseil, an algorithm to generate hybrid explanations. Conseil is also the first algorithm to handle nonmonotonic queries. Experiments on efficiency and explanation quality show that Conseil is comparable and even outperforms previous algorithms. This article extends a previous short conference paper by providing proofs, additional theorems, and a detailed discussion of each step of the Conseil algorithm. It also significantly extends the experimental evaluation on efficiency and explanation quality.