denying the consequent
In conditional reasoning, arguing validly from a hypothetical proposition of the form If p then q that, because q is false, therefore p is false. For example, given the proposition If the burglars entered by the front door, then they forced the lock, it is valid to deduce from the fact that the burglars did not force the lock that they did not enter by the front door. Also called modus tollens. Compare affirming the antecedent, affirming the consequent, denying the antecedent.