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The Hierarchy of Hyperlogics

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Version 2 2023-12-11, 20:11
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conference contribution
posted on 2023-12-11, 20:11 authored by Norine CoenenNorine Coenen, Bernd FinkbeinerBernd Finkbeiner, Christopher Hahn, Jana Hofmann
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.


Preferred Citation

Norine Coenen, Bernd Finkbeiner, Christopher Hahn and Jana Hofmann. The Hierarchy of Hyperlogics. In: IEEE Symposium on Logic in Computer Science (LICS). 2019.

Primary Research Area

  • Reliable Security Guarantees

Name of Conference

IEEE Symposium on Logic in Computer Science (LICS)

Legacy Posted Date


Open Access Type

  • Unknown


@inproceedings{cispa_all_3074, title = "The Hierarchy of Hyperlogics", author = "Coenen, Norine and Finkbeiner, Bernd and Hahn, Christopher and Hofmann, Jana", booktitle="{IEEE Symposium on Logic in Computer Science (LICS)}", year="2019", }

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