Directionality effect in deductive reasoning is a very well-known phenomenon that shows that the percentage of forward or backward inferences that participants make depends on the conditional form used. A new extension of the semantic hypothesis (Oberauer & Wilhelm, 2000) is presented to explain the directionality effect in double conditionals with different directionality. This hypothesis claims that the directional effect depends on which term plays the role of relatum. It also makes several novel claims which have been confirmed in three experiments: Experiments 1 and 2 showed there were more forward than backward inferences when the end-term that played the role of relatum was in the first premise, experiment 1: t (45) = 2.73, p < .01, experiment 2: t (38) = 12.06, p < .05, but there were more backward than forward inferences when the end-term that played the role of relatum was in the second premise, experiment 1: t (45) = 2.84, p < .01, experiment 2: t (38) = 2.21, p < .04. Experiment 3 showed that there was no directional effect when both end-terms played the role of relatum, t (34) = 1.39, p = .17, or when both middle-terms (or neither of the end-terms) played the role of relatum, t (34) = .78, p = .44. These experiments confirmed the predictions of the new extension of the semantic hypothesis.