 In Pizzi and Williamson 1997, a conditional satisfying (i) and (ii) is called an analytic consequential implication and the notion of a normal system of analytic consequential implication is defined. ‘Normal’ here means that such a system contains certain formulas and is closed under certain rules. The smallest normal consequential logic that satisfies AT is called CI. Alternatively, CI can be characterized as the smallest normal system that satisfies the Weak Boethius’ Thesis, i.e, (A → B) ⊃ ¬(A → ¬ B), where → is consequential implication and ¬ is classical negation. In Omori and Wansing 2019 the semantics of CI is presented in a way showing that the semantics of the consequential conditional is obtained by tweaking the truth conditions of strict implication in Kripke models with a serial accessibility relation (so that □A ⊃ ◊A is valid). The standard truth conditions are supplemented by requiring equal modal status for the antecedent and the consequent.