Paradoxical inferences, biconditional interpretation, and exclusivity

Two inferences correct in classical logic are controversial in cognitive science. The reason is that people do not always deem them as valid inferences. One of them is the rule to introduce a conditional. The other one is the rule to introduce a disjunction. The theory of mental models has an account for them. Their conclusions refer to models, and, in both cases, one of those models is inconsistent with the premise. When semantics modulates and removes the incoherent model, the inferences are accepted as correct. The present paper tries to describe those phenomena within the framework of first-order predicate logic. It proposes that the rule to introduce a conditional is not admitted when the conclusion is not a conditional, but a biconditional. It also claims that the rule to introduce a disjunction is not accepted when the disjunction is exclusive.