Conditionals and directionality: on the meaning of if vs. only if

The aim of this study was to test the predictions of the current theories of reasoning about the comprehension of conditional statements. We used two types of conditional statement that are logically equivalent: if p then q and p only if q. The model theory of reasoning considers that these conditional forms differ in their initial meaning, because the negative contingency is considered only in the p only if q form. Mental-rule theories maintain that the interpretation of p only if q depends on a rephrasing of the statement as: if not q then not p. Alternatively, a directional bias may explain the differences between if p then q and p only if q. We report three experiments that demonstrate the existence of a directional bias in the comprehension of the conditionals. The results were not predicted by either the mental-rules theories or the model theory; they could, however, be easily assimilated by the model theory.