Axioms for obligation and robustness with temporal logic

Authors:
Tim French;John C. McCabe-Dansted;Mark Reynolds
Affiliations:
School of Computer Science and Software Engineering, The University of Western Australia, Australia;School of Computer Science and Software Engineering, The University of Western Australia, Australia;School of Computer Science and Software Engineering, The University of Western Australia, Australia
Venue:
DEON'10 Proceedings of the 10th international conference on Deontic logic in computer science
Year:
2010

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Abstract

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.