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Differential Dynamic Logic for Hybrid Systems
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  • Published: 20 August 2008

Differential Dynamic Logic for Hybrid Systems

  • André Platzer1 

Journal of Automated Reasoning volume 41, pages 143–189 (2008)Cite this article

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A Correction to this article was published on 15 November 2021

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Abstract

Hybrid systems are models for complex physical systems and are defined as dynamical systems with interacting discrete transitions and continuous evolutions along differential equations. With the goal of developing a theoretical and practical foundation for deductive verification of hybrid systems, we introduce a dynamic logic for hybrid programs, which is a program notation for hybrid systems. As a verification technique that is suitable for automation, we introduce a free variable proof calculus with a novel combination of real-valued free variables and Skolemisation for lifting quantifier elimination for real arithmetic to dynamic logic. The calculus is compositional, i.e., it reduces properties of hybrid programs to properties of their parts. Our main result proves that this calculus axiomatises the transition behaviour of hybrid systems completely relative to differential equations. In a case study with cooperating traffic agents of the European Train Control System, we further show that our calculus is well-suited for verifying realistic hybrid systems with parametric system dynamics.

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  • 15 November 2021

    A Correction to this paper has been published: https://doi.org/10.1007/s10817-021-09608-w

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Authors and Affiliations

  1. Department of Computing Science, University of Oldenburg, 26111, Oldenburg, Germany

    André Platzer

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  1. André Platzer
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Correspondence to André Platzer.

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The original online version of this article was revised due to retrospective open access order

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Platzer, A. Differential Dynamic Logic for Hybrid Systems. J Autom Reasoning 41, 143–189 (2008). https://doi.org/10.1007/s10817-008-9103-8

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  • Received: 23 August 2007

  • Accepted: 27 June 2008

  • Published: 20 August 2008

  • Issue Date: August 2008

  • DOI: https://doi.org/10.1007/s10817-008-9103-8

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Keywords

  • Dynamic logic
  • Differential equations
  • Sequent calculus
  • Axiomatisation
  • Automated theorem proving
  • Verification of hybrid systems
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