How to eliminate illusions in quantified reasoning

The mental model theory postulates that reasoners build models of situations described in premises that make explicit only what is true according to the premises, and predicts the existence of illusions in inferences, which are believed to have compelling but erroneous conclusions.

Abstract

The mental model theory postulates that reasoners build models of situations described in premises. These models normally make explicit only what is true according to the premises. The theory has an unexpected consequence. It predicts the existence of illusions in inferences: Certain inferences should have compelling but erroneous conclusions. Previous studies have corroborated the existence of such illusions. The present study reports the first effective antidote to them. For example, most people incorrectly answer "yes" to the following problem: Only one of the following statements is true ... /At least some of the plastic beads are not red./None of the plastic beads are red./Is it possible that none of the red beads are plastic? In two experiments, we progressively eliminated this fallacy and others by using instructions designed to overcome the bias toward truth. The difference between the illusory and the control problems disappeared when the participants were instructed to work out both the case in which the first premise was true and second premise was false and the case in which the second premise was true and the first premise was false.