An experiment is reported in which participants were asked to record how confident they felt about the correctness of their responses as they assessed the validity of deductive arguments whose conclusions varied in prior believability. The results showed that participants were more confident of their responses to valid problems than invalid problems irrespective of believability status, providing support for the idea that invalid problems are more demanding to process than valid problems. Effects of belief, logic on conclusion acceptance rates and a logicxbelief interaction are also demonstrated, and evidence is provided to suggest that belief bias principally reflects a tendency to reject unbelievable arguments. A theory is proposed in which belief bias effects are accounted for by the variations in the processing demands of valid and invalid syllogisms.