In the distributed and dynamic framework of the Web, data quality is a big challenge. The Linked Open Data (LOD) provides an enormous amount of data, the quality of which is difficult to control. Quality is intrinsically a matter of usage, so consumers need ways to specify quality rules that make sense for their use, in order to get only data conforming to these rules. We propose a user-side query framework equipped with a checker of constraints and confidence levels on data resulting from LOD providers\' query evaluations. We detail its theoretical foundations and we provide experimental results showing that the check additional cost is reasonable and that integrating the constraints in the queries further improves it significantly.