Unifying Hyper and Epistemic Temporal Logic

Abstract

In the literature, two powerful temporal logic formalisms have been proposed for expressing information flow security requirements, that in general, go beyond regular properties. One is classic, based on the knowledge modalities of epistemic logic. The other one, the so called hyper logic, is more recent and subsumes many proposals from the literature; it is based on explicit and simultaneous quantification over multiple paths. In an attempt to better understand how these logics compare with each other, we consider the logic KCTL* (the extension of CTL* with knowledge modalities and synchronous perfect recall semantics) and HyperCTL*. We first establish that KCTL* and HyperCTL* are expressively incomparable. Second, we introduce and study a natural linear past extension of HyperCTL* to unify KCTL* and HyperCTL*; indeed, we show that KCTL* can be easily translated in linear time into the proposed logic. Moreover, we show that the model-checking problem for this novel logic is decidable, and we provide its exact computational complexity in terms of a new measure of path quantifiers' alternation. For this, we settle open complexity issues for unrestricted quantified propositional temporal logic.