(2019) The Hierarchy of Hyperlogics.
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Abstract
Hyperproperties, which generalize trace properties by relating multiple traces, are widely studied in information-flow security. Recently, a number of logics for hyperproperties have been proposed, and there is a need to understand their decidability and relative expressiveness. The new logics have been obtained from standard logics with two principal extensions: temporal logics, like LTL and CTL∗, have been generalized to hyperproperties by adding variables for traces or paths. First-order and second-order logics, like monadic first-order logic of order and MSO, have been extended with the equal-level predicate. We study the impact of the two extensions across the spectrum of linear-time and branching-time logics, in particular for logics with quantification over propositions. The resulting hierarchy of hyperlogics differs significantly from the classical hierarchy, suggesting that the equal-level predicate adds more expressiveness than trace and path variables. Within the hierarchy of hyperlogics, we identify new boundaries on the decidability of the satisfiability problem. Specifically, we show that while HyperQPTL and HyperCTL∗ are both undecidable in general, formulas within their ∃∗∀∗ fragments are decidable.
| Item Type: | Conference or Workshop Item (A Paper) (Paper) |
|---|---|
| Conference: | LICS IEEE Symposium on Logic in Computer Science |
| Depositing User: | Bernd Finkbeiner |
| Date Deposited: | 25 May 2020 11:28 |
| Last Modified: | 11 May 2021 13:54 |
| Primary Research Area: | NRA2: Reliable Security Guarantees |
| URI: | https://publications.cispa.saarland/id/eprint/3074 |
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