Rationality, transitivity, and contraposition

Four weak forms of Transitivity are presented that, in preferential logic, are equivalent to Rational Monotonicity and a weak form of Contraposition that is strictly weaker than RationalMonotonicity but equivalent to it in the presence of Disjunctive Rationality.

Abstract

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.