A temporal logic of robustness / John C. McCabe-Dansted

2011

This thesis presents a new temporal logic of robustness, called Robust Full Computation Tree Logic (RoCTL*) which adds operators for obligation and robustness to the commonly used Full Computation Tree Logic (CTL*). The RoCTL* logic is for reasoning about how robustly a reactive system can ensure that various goals are met in the face of occasional violations of the norms describing the correct behaviour of the system. Such violations may involve, for example network outages or human error. Whereas logics of reliability typically use probabilities, RoCTL* represents robustness in terms of the number of discrete violations that the system can handle while still ensuring some goal is met. As probabilities are often implementation dependant, RoCTL* may be more suited to reasoning about reactive systems in the abstract than existing logics of reliability.

Having introduced RoCTL*, we study this logic in terms of expressivity, computational complexity and formal systems. We prove that all properties that can be expressed in RoCTL* can be expressed in the original CTL* logic, but also that the RoCTL* logic can express some properties much more succinctly than CTL*. We will present a tableau based decision procedure for a variant of RoCTL*. We also discuss ways of deciding the satisfiability of RoCTL* formulae by translating RoCTL* into other logics and into tree-automata. As these decision procedures are non-elementary, we also propose a CTL-like restriction of RoCTL* that has similar complexity to CTL and is thus a practical logic to compute. We present axiomatisations of fragments of RoCTL*. We find that the axiomatisation of the operator for obligation in RoCTL* matches that of an existing logic called Deontic S5 (or KD45). We examine some existing philosophical arguments for use of Deontic S5 as a component of combined logics for normative reasoning. These arguments may explain why RoCTL* is expressive enough to express the softconstraints considered in this thesis.

Thesis (Ph.D.)--University of Western Australia, 2011

http://repository.uwa.edu.au:80/R/-?func=dbin-jump-full&object_id=30098&silo_library=GEN01