@article {3152435, title = {Reactive standard deontic logic}, journal = {Journal of Logic and Computation}, volume = {25}, number = {1}, year = {2013}, pages = {117{\textendash}157}, 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 {\textrightarrow} represent the accessibility relation between worlds, reactive models add two elements: arrows {\textrightarrow} are labelled as ‘active’ or ‘inactive’, and double arrows \&8608; connect arrows, e.g. (x1 {\textrightarrow} x2) \&\#8608; (x3 {\textrightarrow} x4). The idea is that passing through x1 {\textrightarrow} x2 activates a switch represented by \&8608; that inverts the label of x3 {\textrightarrow} 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.

}, issn = {0955-792X}, doi = {http://dx.doi.org/10.1093/logcom/exs043}, author = {Gabbay, Dov M. and Stra{\ss}er, Christian} }