Reasoning about possibilities is fundamental in daily life and inartificial intelligence. It is formalized in modal logics, of whichthere are infinitely many. Two experiments showed thatindividuals make inferences that are parsimonious aboutpossibilities, and that they reject conclusions referring topossibilities that the premises do not support. Both sorts ofinference contravene modal logics, i.e., the simplest system ofmodal logic and the infinite number of systems based on it.

The mental model theory postulates that reasoners build models of the situations described in premises, and that these models normally make explicit only what is true. A computer program revealed an unexpected consequence of the theory: it predicts that certain inferences should have compelling but erroneous conclusions. Two experiments corroborated the existence of such illusions in inferences about what is possible given quantified assertions, such as 'At least some of the plastic beads are not red.' Experiment 1 showed that, as predicted, participants erroneously inferred that impossible assertions were possible, and that possible situations were impossible, but they performed well with control problems. Experiment 2 demonstrated the existence of similar illusions in inferences from dyadic assertions, e.g. 'All the boys played with the girls'.