Skip to main content
SpringerLink
Log in

Spatial Reasoning About Motorway Traffic Safety with Isabelle/HOL

  • Conference paper
  • First Online:
Integrated Formal Methods (IFM 2017)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 10510))

Included in the following conference series:

Abstract

Formal verification of autonomous vehicles on motorways is a challenging problem, due to the complex interactions between dynamical behaviours and controller choices of the vehicles. In previous work, we showed how an abstraction of motorway traffic, with an emphasis on spatial properties, can be beneficial. In this paper, we present a semantic embedding of a spatio-temporal multi-modal logic, specifically defined to reason about motorway traffic, into Isabelle/HOL. The semantic model is an abstraction of a motorway, emphasising local spatial properties, and parameterised by the types of sensors deployed in the vehicles. We use the logic to define controller constraints to ensure safety, i.e., the absence of collisions on the motorway. After proving safety with a restrictive definition of sensors, we relax these assumptions and show how to amend the controller constraints to still guarantee safety.

This work was supported by the EPSRC Research Programme EP/N007565/1 Science of Sensor System Software (S4).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    The code of the formalisation can be found at www.github.com/svenlinker/HMLSL. It is compatible with Isabelle2016-1.

  2. 2.

    The function \( Abs\_nat\_int \) takes a set of natural numbers as its input, and returns an element of type \( nat\_int \). It is automatically created by Isabelle as a result of the type definition in Sect. 2.2. Subsequently, we will silently omit these functions.

References

  1. Hilscher, M., Linker, S., Olderog, E.-R., Ravn, A.P.: An abstract model for proving safety of multi-lane traffic manoeuvres. In: Qin, S., Qiu, Z. (eds.) ICFEM 2011. LNCS, vol. 6991, pp. 404–419. Springer, Heidelberg (2011). doi:10.1007/978-3-642-24559-6_28

    Chapter  Google Scholar 

  2. Linker, S., Hilscher, M.: proof theory of a multi-lane spatial logic. LMCS 11 (2015)

    Google Scholar 

  3. Linker, S.: Proofs for traffic safety: combining diagrams and logic. Ph.D. thesis, University of Oldenburg (2015). http://oops.uni-oldenburg.de/2337/

  4. Nipkow, T., Paulson, L.C., Wenzel, M.: Isabelle/HOL–A Proof Assistant for Higher-Order Logic. LNCS, vol. 2283. Springer, Heidelberg (2002)

    MATH  Google Scholar 

  5. Platzer, A., Quesel, J.-D.: KeYmaera: a hybrid theorem prover for hybrid systems (system description). In: Armando, A., Baumgartner, P., Dowek, G. (eds.) IJCAR 2008. LNCS (LNAI), vol. 5195, pp. 171–178. Springer, Heidelberg (2008). doi:10.1007/978-3-540-71070-7_15

    Chapter  Google Scholar 

  6. Loos, S.M., Platzer, A., Nistor, L.: Adaptive cruise control: hybrid, distributed, and now formally verified. In: Butler, M., Schulte, W. (eds.) FM 2011. LNCS, vol. 6664, pp. 42–56. Springer, Heidelberg (2011). doi:10.1007/978-3-642-21437-0_6

    Chapter  Google Scholar 

  7. Platzer, A.: The complete proof theory of hybrid systems. In: LICS, pp. 541–550. IEEE (2012)

    Google Scholar 

  8. Rizaldi, A., Althoff, M.: Formalising traffic rules for accountability of autonomous vehicles. In: ITSC, pp. 1658–1665. IEEE (2015)

    Google Scholar 

  9. Kamali, M., Dennis, L.A., McAree, O., Fisher, M., Veres, S.M.: Formal verification of autonomous vehicle platooning. arXiv preprint arXiv:1602.01718 (2016)

  10. Alur, R., Dill, D.L.: A theory of timed automata. TCS 126, 183–235 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  11. Dennis, L.A., Fisher, M., Webster, M.P., Bordini, R.H.: Model checking agent programming languages. ASE 19, 5–63 (2012)

    Google Scholar 

  12. Larsen, K.G., Pettersson, P., Yi, W.: Uppaal in a nutshell. STTT 1, 134–152 (1997)

    Article  MATH  Google Scholar 

  13. Campbell, J., Tuncali, C.E., Liu, P., Pavlic, T.P., Ozguner, U., Fainekos, G.: Modeling concurrency and reconfiguration in vehicular systems: a \(\pi \)-calculus approach. In: CASE, pp. 523–530 IEEE (2016)

    Google Scholar 

  14. Alur, R.: Principles of Cyber-Physical Systems. MIT Press, Cambridge (2015)

    Google Scholar 

  15. Braüner, T.: Hybrid Logic and Its Proof-Theory. Springer, Netherlands (2010)

    MATH  Google Scholar 

  16. Moszkowski, B.C.: A temporal logic for multilevel reasoning about hardware. Computer 18, 10–19 (1985)

    Article  Google Scholar 

  17. Benzmüller, C., Paulson, L.: Quantified multimodal logics in simple type theory. Log. Univers. 7, 7–20 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  18. Bochmann, G.V., Hilscher, M., Linker, S., Olderog, E.R.: Synthesizing and verifying controllers for multi-lane traffic maneuvers. FAC 29, 583–600 (2017)

    MathSciNet  Google Scholar 

  19. Olderog, E.-R., Ravn, A.P., Wisniewski, R.: Linking discrete and continuous models, applied to traffic manoeuvrers. In: Hinchey, M.G., Bowen, J.P., Olderog, E.-R. (eds.) Provably Correct Systems. NMSSE, pp. 95–120. Springer, Cham (2017). doi:10.1007/978-3-319-48628-4_5

    Chapter  Google Scholar 

  20. Hölzl, J.: Markov processes in Isabelle/HOL. In: CPP 2017, pp. 100–111. ACM (2017)

    Google Scholar 

  21. Hilscher, M., Linker, S., Olderog, E.-R.: Proving safety of traffic manoeuvres on country roads. In: Liu, Z., Woodcock, J., Zhu, H. (eds.) Theories of Programming and Formal Methods. LNCS, vol. 8051, pp. 196–212. Springer, Heidelberg (2013). doi:10.1007/978-3-642-39698-4_12

    Chapter  Google Scholar 

  22. Hilscher, M., Schwammberger, M.: An abstract model for proving safety of autonomous urban traffic. In: Sampaio, A., Wang, F. (eds.) ICTAC 2016. LNCS, vol. 9965, pp. 274–292. Springer, Cham (2016). doi:10.1007/978-3-319-46750-4_16

    Chapter  Google Scholar 

  23. Xu, B., Li, Q.: A spatial logic for modeling and verification of collision-free control of vehicles. In: ICECCS, pp. 33–42. IEEE (2016)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Liverpool, Liverpool, UK

    Sven Linker

Authors
  1. Sven Linker
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sven Linker .

Editor information

Editors and Affiliations

  1. Massachusetts Institute of Technology, Cambridge, Massachusetts, USA

    Nadia Polikarpova

  2. University of Surrey, Guildford, United Kingdom

    Steve Schneider

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Linker, S. (2017). Spatial Reasoning About Motorway Traffic Safety with Isabelle/HOL. In: Polikarpova, N., Schneider, S. (eds) Integrated Formal Methods. IFM 2017. Lecture Notes in Computer Science(), vol 10510. Springer, Cham. https://doi.org/10.1007/978-3-319-66845-1_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-66845-1_3

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-66844-4

  • Online ISBN: 978-3-319-66845-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation