Summary: The result quality of queries incorporating impreciseness can be improved by the specification of user-defined weights. Existing approaches evaluate weighted queries by applying arithmetic evaluations on top of the query’s intrinsic logic. This complicates the usage of logic-based optimization. Therefore, we suggest a weighting approach that is completely embedded in a logic. In order to facilitate the user interaction with the system, we exploit the intuitively comprehensible concept of preferences. In addition, we use a machine-based learning algorithm to learn weighting values in correspondence to the user’s intended semantics of a posed query. Experiments show the utility of our approach.