Abstract  We introduce a reactive variant of SDL (standard deontic logic): SDLR1 (reactive standard deontic logic). Given a Kripkean view on the semantics of SDL in terms of directed graphs where arrows → represent the accessibility relation between worlds, reactive models add two elements: arrows → are labelled as active or inactive, and double arrows &8608; connect arrows, e.g. (x_{1} → x_{2}) &\#8608; (x_{3} → x_{4}). The idea is that passing through x_{1} → x_{2} activates a switch represented by &8608; that inverts the label of x_{3} → x_{4} and hence activates respectively deactivates this arrow. This allows to introduce two modalities: &\#9633; is the usual KDmodality of SDL and operates on the Kripkean graph where all labels and double arrows are ignored, while &\#8709; takes them into account. We demonstrate that RSDL1 allows for an intuitive interpretation of ought. The logic can handle contrarytoduty cases such as several instantiations of the Chisholm set in a paradoxfree way by means of using double arrows and annotations to block and give access to ideal worlds.
