We present a robust method for gathering relational facts from the Web, based on matching generalized patterns which are automatically learned from seed facts for relations of interest. Our approach combines these generalized patterns for high recall information extraction with a rule-based, declarative reasoning approach to also ensure high precision. Newly extracted candidate facts are assigned statistical weights which reflect the strengths of the patterns used to extract them. For checking the plausibility of candidate facts with respect to existing knowledge and competing hypotheses, we use an efficient algorithm for weighted Max-Sat over propositional-logic clauses. In contrast to prior work on reasoning-based information extraction, we employ richer statistics and smart pruning to bound the number of grounded rules passed on to the Max-Sat solver.