Skip to main content

Towards a Unifying Framework for Uncertainty in Cyber-Physical Systems

  • Chapter
  • First Online:
Applicable Formal Methods for Safe Industrial Products

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14165))

  • 192 Accesses

Abstract

This paper is dedicated with affection to Jan Peleska on the occasion of his 65th birthday. We discuss a unifying theory of uncertainty in robotics based on Hoare & He’s unifying theories of programming and Hehner’s probabilistic predicative programming. We start a long-term research agenda with a semantics for Prism and end with many questions.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 59.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 74.99
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

References

  1. Alur, R., Henzinger, T.A.: Reactive modules. Formal Methods Syst. Des. 15(1) (1999)

    Google Scholar 

  2. Back, R.-J., von Wright, J.: Refinement Calculus – A Systematic Introduction. Graduate Texts in Computer Science. Springer (1998). https://doi.org/10.1007/978-1-4612-1674-2

  3. Casella, G., Robert, C.P., Wells, M.T.: Generalized Accept-Reject Sampling Schemes. University of Michigan, Institute of Mathematical Statistics Lecture Notes Series (2004)

    Google Scholar 

  4. Cavalcanti, A., Huang, W., Peleska, J., Woodcock, J.: CSP and kripke structures. In: Leucker, M., Rueda, C., Valencia, F.D. (eds.) ICTAC 2015. LNCS, vol. 9399, pp. 505–523. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-25150-9_29

    Chapter  Google Scholar 

  5. Cavalcanti, A., Woodcock, J.: A tutorial introduction to CSP in unifying theories of programming. In: Cavalcanti, A., Sampaio, A., Woodcock, J. (eds.) PSSE 2004. LNCS, vol. 3167, pp. 220–268. Springer, Heidelberg (2006). https://doi.org/10.1007/11889229_6

    Chapter  Google Scholar 

  6. Chandy, K.M., Misra, J.: Parallel Program Design: A Foundation. Addison Wesley (1988)

    Google Scholar 

  7. den Hartog, J., de Vink, E.P.: Verifying probabilistic programs using a Hoare like logic. Int. J. Found. Comput. Sci. 13(3), 315–340 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  8. Dijkstra, E.W.: Guarded commands, nondeterminacy and formal derivation of programs. Commun. ACM 18(8), 453–457 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  9. Edsger, W.: Dijkstra, A Discipline of Programming. Prentice-Hall (1976)

    Google Scholar 

  10. Dijkstra, E.W.: On the reliability of programs. In: Apt, K.R., Hoare, T.D. (eds.) Edsger Wybe Dijkstra: His Life, Work, and Legacy, pp. 359–370. ACM / Morgan & Claypool (2022)

    Google Scholar 

  11. Dill, D.L.: The Murphi verification system. In: Alur, R., Henzinger, T.A. (eds.) CAV 1996. LNCS, vol. 1102, pp. 390–393. Springer, Heidelberg (1996). https://doi.org/10.1007/3-540-61474-5_86

    Chapter  Google Scholar 

  12. Esterle, L., Porter, B., Woodcock, J.: Verification and uncertainties in self-integrating system. In El-Araby, E., Kalogeraki, V. (eds.) IEEE International Conference on Autonomic Computing and Self-Organizing Systems, ACSOS 2021, pp. 220–225. IEEE (2021)

    Google Scholar 

  13. Feinberg, E.A., Shwartz, A. (eds.) Handbook of Markov Decision Processes. Kluwer (2002)

    Google Scholar 

  14. Conserva Filho, M.S., Marinho, R., Mota, A., Woodcock, J.: Analysing robochart with probabilities. In: Massoni, T., Mousavi, M.R. (eds.) SBMF 2018. LNCS, vol. 11254, pp. 198–214. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-03044-5_13

    Chapter  Google Scholar 

  15. Foster, S., Baxter, J., Cavalcanti, A., Woodcock, J., Zeyda, F.: Unifying semantic foundations for automated verification tools in Isabelle/UTP. Sci. Comput. Program. 197, 102510 (2020)

    Article  Google Scholar 

  16. Gabbay, D.M.: Introducing reactive Kripke semantics and arc accessibility. Ann. Math. Artif. Intell. 66(1–4), 7–53 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  17. Floyd, C.: Theory and practice of software development. In: Mosses, P.D., Nielsen, M., Schwartzbach, M.I. (eds.) CAAP 1995. LNCS, vol. 915, pp. 25–41. Springer, Heidelberg (1995). https://doi.org/10.1007/3-540-59293-8_185

    Chapter  MATH  Google Scholar 

  18. Harwood, W., Cavalcanti, A., Woodcock, J.: A theory of pointers for the UTP. In: Fitzgerald, J.S., Haxthausen, A.E., Yenigun, H. (eds.) ICTAC 2008. LNCS, vol. 5160, pp. 141–155. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-85762-4_10

    Chapter  MATH  Google Scholar 

  19. He, J., Seidel, K., McIver, A.: Probabilistic models for the guarded command language. Sci. Comput. Program. 28(2–3), 171–192 (1997)

    MathSciNet  MATH  Google Scholar 

  20. Hehner, E.C.R.: Probabilistic predicative programming. In: Kozen, D. (ed.) MPC 2004. LNCS, vol. 3125, pp. 169–185. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-27764-4_10

    Chapter  Google Scholar 

  21. Hehner, E.C.R.: A probability perspective. Formal Aspects Comput. 23(4), 391–419 (2011)

    Google Scholar 

  22. Hintikka, J.: Knowledge and Belief. Cornell University Press (1962)

    Google Scholar 

  23. Hoare, C.A.R.: An axiomatic basis for computer programming (reprint). Commun. ACM 26(1), 53–56 (1983)

    Article  Google Scholar 

  24. Hoare, C.A.R., Jifeng, H.: Unifying Theories of Programming. Prentice Hall (1998)

    Google Scholar 

  25. Huang, W., Peleska, J.: Complete model-based equivalence class testing. Int. J. Softw. Tools Technol. Transf. 18(3), 265–283 (2016)

    Article  Google Scholar 

  26. Knuth, D., Yao, A.: Algorithms and Complexity: New Directions and Recent Results, chapter The complexity of nonuniform random number generation. Academic Press (1976)

    Google Scholar 

  27. Kwiatkowska, M.Z., Norman, G., Parker, D.: Quantitative analysis with the probabilistic model checker PRISM. In: Cerone, A., Wiklicky, H. (eds.) Proceedings of the Third Workshop on Quantitative Aspects of Programming Languages, QAPL 2005, Edinburgh, UK, 2–3 April 2005, vol. 153. ENTCS, pp. 5–31. Elsevier (2005)

    Google Scholar 

  28. Lauri, M., Hsu, D., Pajarinen, J.: Partially observable Markov decision processes in robotics: A survey. CoRR, abs/ arXiv: 2209.10342 (2022)

  29. McIver, A., Morgan, C.: Correctness by construction for probabilistic programs. In: Margaria, T., Steffen, B. (eds.) ISoLA 2020. LNCS, vol. 12476, pp. 216–239. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-61362-4_12

    Chapter  Google Scholar 

  30. Morgan, C.: Programming from Specifications, 2nd edn., International series in computer science. Prentice Hall (1994)

    Google Scholar 

  31. Morris, J.M.: A theoretical basis for stepwise refinement and the programming calculus. Sci. Comput. Program. 9(3), 287–306 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  32. Prism. The PRISM language — semantics. www.prismmodelchecker.org/doc/semantics.pdf

  33. Shannon, C.L., Weaver, W.: Mathematical Theory of Communication. University of Illinois (1963)

    Google Scholar 

  34. Shilov, N.V., Garanina, N.O.: Combining knowledge and fixpoints. Technical Report Preprint 98, A.P. Ershov Institute of Informatics Systems, Novosibirsk (2002).www.iis.nsk.su/files/preprints/098.pdf

  35. Woodcock, J.C.P.: Properties of Z specifications. ACM SIGSOFT Softw. Eng. Notes 14(5), 43–54 (1989)

    Article  Google Scholar 

  36. Woodcock, J.: Hoare and He’s unifying theories of programming. In: Jones, C.B., Misra, J., (eds.) Theories of Programming: The Life and Works of Tony Hoare, pp. 285–316. ACM / Morgan & Claypool (2021)

    Google Scholar 

  37. Woodcock, J., Cavalcanti, A.: A tutorial introduction to designs in unifying theories of programming. In: Boiten, E.A., Derrick, J., Smith, G. (eds.) IFM 2004. LNCS, vol. 2999, pp. 40–66. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24756-2_4

    Chapter  Google Scholar 

  38. Woodcock, J., Cavalcanti, A., Foster, S., Mota, A., Ye, K.: Probabilistic semantics for robochart. In: Ribeiro, P., Sampaio, A. (eds.) UTP 2019. LNCS, vol. 11885, pp. 80–105. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-31038-7_5

    Chapter  Google Scholar 

  39. Woodcock, J., Davies, J.: Using Z – Specification, Refinement, and Proof. Prentice Hall international series in computer science. Prentice Hall (1996)

    Google Scholar 

  40. Woodcock, J., Gomes, C., Macedo, H.D., Larsen, P.G.: Uncertainty quantification and runtime monitoring using environment-aware digital twins. In: Margaria, T., Steffen, B. (eds.) ISoLA 2020. LNCS, vol. 12479, pp. 72–87. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-83723-5_6

    Chapter  Google Scholar 

  41. Ye, K., Cavalcanti, A., Foster, S., Miyazawa, A., Woodcock, J.: Probabilistic modelling and verification using RoboChart and PRISM. Softw. Syst. Model. 21(2), 667–716 (2022)

    Article  Google Scholar 

  42. Ye, K., Foster, S., Woodcock, J.: Automated reasoning for probabilistic sequential programs with theorem proving. In: Fahrenberg, U., Gehrke, M., Santocanale, L., Winter, M. (eds.) RAMiCS 2021. LNCS, vol. 13027, pp. 465–482. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-88701-8_28

    Chapter  Google Scholar 

Download references

Acknowledgements

This work has benefited from extensive discussions with Radu Calinescu, Ana Cavalcanti, Simon Foster, Rob Hierons, Peter Gorm Larsen, Zhiming Liu, Mohammad Mousavi, and Kangfeng Ye. The work is supported by (i) EPSRC EP/R025479/1 RoboTest: Systematic model-based testing and simulation of mobile autonomous robots; and (ii) EPSRC EP/V026801/2 UKRI Trustworthy Autonomous Systems Node in Verifiability.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jim Woodcock .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Woodcock, J. (2023). Towards a Unifying Framework for Uncertainty in Cyber-Physical Systems. In: Haxthausen, A.E., Huang, Wl., Roggenbach, M. (eds) Applicable Formal Methods for Safe Industrial Products. Lecture Notes in Computer Science, vol 14165. Springer, Cham. https://doi.org/10.1007/978-3-031-40132-9_15

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-40132-9_15

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-40131-2

  • Online ISBN: 978-3-031-40132-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics