Rationality, transitivity, and contraposition

The purpose of this note is to compare the rule of Rational Monotonicity proposed in [3] and different rules expressing some weak forms of Transitivity and Contraposition. We present four weak forms of Transitivity that, in preferential logic, are equivalent to Rational Monotonicity and a weak form of Contraposition that is strictly weaker than Rational Monotonicity but equivalent to it in the presence of Disjunctive Rationality.