Axioms for obligation and robustness with temporal logic

RoCTL* was proposed to model and specify the robustness of reactive systems. RoCTL* extended CTL* with the addition of Obligatory and Robustly operators, which quantify over failure-free paths and paths with one more failure respectively. This paper gives an axiomatisation for all the operators of RoCTL* with the exception of the Until operator; this fragment is able to express similar contrary-to-duty obligations to the full RoCTL* logic. We call this formal system NORA, and give a completeness proof. We also consider the fragments of the language containing only path quantifiers (but where variables are dependent on histories). We examine semantic properties and potential axiomatisations for these fragments.