On the Logic of Normative Systems

Thomas Ågotnes, Wiebe van der Hoek, Juan A. Rodríguez-Aguilar, Carles Sierra, Michael Wooldridge

We introduce Normative Temporal Logic (NTL), a logic for reasoning about normative systems. NTL is a generalisation of the well-known branching-time temporal logic CTL, in which the path quantifiers A ("on all paths...") and E ("on some path") are replaced by the indexed deontic operators O_n and P_n, where for example "O_n Phi" means "Phi is obligatory in the context of normative system n". 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 P-complete up to ExpTime-hard for these variations.