TY - JOUR T1 - Reactive standard deontic logic JF - Journal of Logic and Computation Y1 - 2013 A1 - Gabbay, Dov M. A1 - Straßer, Christian AB -

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. (x1 → x2) &\#8608; (x3 → x4). The idea is that passing through x1 → x2 activates a switch represented by &8608; that inverts the label of x3 → x4 and hence activates respectively deactivates this arrow. This allows to introduce two modalities: &\#9633; is the usual KD-modality 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 contrary-to-duty cases such as several instantiations of the Chisholm set in a paradox-free way by means of using double arrows and annotations to block and give access to ideal worlds.

VL - 25 SP - 117–157 ER -