DeepAI

# The Hierarchy of Hyperlogics

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.

• 8 publications
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07/06/2022

### Expressiveness and Decidability of Temporal Logics for Asynchronous Hyperproperties

Hyperproperties are properties of systems that relate different executio...
02/01/2022

### First-order Temporal Logic on Finite Traces: Semantic Properties, Decidable Fragments, and Applications

Formalisms based on temporal logics interpreted over finite strict linea...
05/31/2019

### Synthesizing Reactive Systems from Hyperproperties

We study the reactive synthesis problem for hyperproperties given as for...
06/15/2018

### Flow Logic

Flow networks have attracted a lot of research in computer science. Inde...
03/06/2020

### Teaching Temporal Logics to Neural Networks

We show that a deep neural network can learn the semantics of linear-tim...
06/23/2022

### Towards a Model Theory of Ordered Logics: Expressivity and Interpolation (Extended version)

We consider the family of guarded and unguarded ordered logics, that con...
07/02/2018

### Monitoring Hyperproperties

Hyperproperties, such as non-interference and observational determinism,...