This article describes a new theory of propositional reasoning, that is, deductions depending on if, or, and, and not. The theory proposes that reasoning is a semantic process based on mental models. It assumes that people are able to maintain models of only a limited number of alternative states of affairs, and they accordingly use models representing as much information as possible in an implicit way. They represent a disjunctive proposition, such as "There is a circle or there is a triangle," by imagining initially 2 alternative possibilities: one in which there is a circle and the other in which there is a triangle. This representation can, if necessary, be fleshed out to yield an explicit representation of an exclusive or an inclusive disjunction. The theory elucidates all the robust phenomena of propositional reasoning. It also makes several novel predictions, which were corroborated by the results of 4 experiments.