We report 3 experiments investigating novel sorts of inference, such as: A or B or both. Therefore, possibly (A and B). Where the contents were sensible assertions, for example, "Space tourism will achieve widespread popularity in the next 50 years or advances in material science will lead to the development of antigravity materials in the next 50 years, or both." Most participants accepted the inferences as valid, though they are invalid in modal logic and in probabilistic logic too. But, the theory of mental models predicts that individuals should accept them. In contrast, inferences of this sort--A or B but not both. Therefore, A or B or both--are both logically valid and probabilistically valid. Yet, as the model theory also predicts, most reasoners rejected them. The participants' estimates of probabilities showed that their inferences tended not to be based on probabilistic validity, but that they did rate acceptable conclusions as more probable than unacceptable conclusions. We discuss the implications of the results for current theories of reasoning.