Incompleteness due to missing attribute values (aka "null values") is very common in autonomous web databases, on which user accesses are usually supported through mediators. Traditional query processing techniques that focus on the strict soundness of answer tuples often ignore tuples with critical missing attributes, even if they wind up being relevant to a user query. Ideally we would like the mediator to retrieve such possible answers and gauge their relevance by accessing their likelihood of being pertinent answers to the query. The autonomous nature of web databases poses several challenges in realizing this objective. Such challenges include the restricted access privileges imposed on the data, the limited support for query patterns, and the bounded pool of database and network resources in the web environment. We introduce a novel query rewriting and optimization framework QPIAD that tackles these challenges. Our technique involves reformulating the user query based ...