The use of logic in question answering (QA) promises better accuracy of results, better utilization of the document collection, and a straightforward solution for integrating background knowledge. However, the brittleness of the logical approach still hinders its breakthrough into applications. Several proposals exist for making logic-based QA more robust against erroneous results of linguistic analysis and against gaps in the background knowledge: Extracting useful information from failed proofs, embedding the prover in a relaxation loop, and fusion of logic-based and shallow features using machine learning (ML). In the paper, we explore the effectiveness of these techniques for logic-based passage filtering in the LogAnswer question answering system. An evaluation on factual question of QA@CLEF07 reveals a precision of 54.8% and recall of 44.9% when relaxation results for two distinct provers are combined.