On the Logic of Normative Systems

We introduce emph{Normative Temporal Logic} (acro{ntl}), a logic for reasoning about normative systems. acro{ntl} is a generalisation of the well-known branching-time temporal logic acro{ctl}, in which the path quantifiers $Apath$ (``on all pathsldots'') and $Epath$ (``on some pathldots'') are replaced by the indexed deontic operators $O{ s}$ and $P{ s}$, where for example $O{ s}phi$ means ``$phi$ is obligatory in the context of normative system $ s$''. After defining the logic, we give a sound and complete axiomatisation, and discuss the logic's relationship to standard deontic logics. We present a symbolic representation language for models and normative systems, and identify four different model checking problems, corresponding to whether or not a model is represented symbolically or explicitly, and whether or not we are given an interpretation for the normative systems named in formulae to be checked. We show that the complexity of model checking varies from acro{p}-complete up to acro{exptime}-hard for these variations.