The effect of explicit negatives and of different contrast classes on conditional syllogisms

One experiment tested the effects of systematically negating the constituen ts of four fundamental inferences based on conditionals: Modus Ponens (i.e. inferences of the form: if p then q; p therefore q), Modus Tollens (if p t hen q; not-q therefore not-p); Affirmation of the Consequent (if p then q; q therefore p), and Denial of the Antecedent (if p then q; not-p therefore not-q). The latter two inferences are valid only for bi-conditionals (if, a nd only if, p then q). The participants drew their own conclusions from pre mises about letters and numbers on cards. We observed a significant effect of explicit negatives on Modus Tollens and Denial of the Antecedent problem s: The inferences were drawn more often for conditionals that yield a negat ive conclusion (e.g. ii p then not q; q therefore not p) than for condition als that yield an affirmative conclusion (e.g. if not p then q; not q there fore p). Additionally, we observed a similar, but smaller effect on Affirma tion of the Consequent problems. Furthermore, we observed a significant eff ect of the categorical premise (affirmative or negative), especially on Aff irmation of the Consequent problems. Finally, we observed an effect of the magnitude of the contrast class. If the contrast is larger (a set of three, five or nine values), then the making of a double negation or the producti on of an affirmative conclusion is more difficult for Denial of the Anteced ent inferences. We discussed the results in relation to a negative categori cal premise bias, an affirmative premise bias, a negative conclusion bias a nd a double negation effect.