The theory of mental models postulates that disjunctions of the sort, A or B, where A and B are sensible everyday clauses, have a core meaning that allows an inclusive interpretation, referring to three possibilities: A and not-B, not-A and B, and A and B. The meaning of the clauses and knowledge can modulate this meaning by blocking the construction of at least one model of a possibility—for example, “Rui is playing tennis or he is surfing” blocks the model of Rui doing both activities. This theory is implemented in a computer program. Three experiments investigated the core interpretation and interpretations in which the contents of the clauses should block the model of A and B (as in the preceding example), the model of A and not-B, or the model of not-A and B. In Experiment 1, the participants listed the possibilities for each of the four sorts of disjunction. The results corroborated the predicted modulations. In Experiment 2, these predicted interpretations governed the conclusions that participants accepted from disjunctions and categorical premises. In Experiment 3, the predicted interpretations yielded reliable effects on the conclusions that the participants drew for themselves. We relate these results to theories of reasoning.