Journal of Logic and Computation

TitleReactive standard deontic logic
Publication TypeJournal Article
Year of Publication2013
AuthorsGabbay, DM, Straßer, C
JournalJournal of Logic and Computation
Volume25
Number1
Pagination117–157
ISSN0955-792X
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. (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.

DOI10.1093/logcom/exs043
Citation Key3152435
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