Advertisement

Three-Valued Spatio-Temporal Logic: A Further Analysis on Spatio-Temporal Properties of Stochastic Systems

  • Ludovica Luisa Vissat
  • Michele Loreti
  • Laura Nenzi
  • Jane Hillston
  • Glenn Marion
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10503)

Abstract

In this paper we present Three-Valued Spatio-Temporal Logic (TSTL), which enriches the available spatio-temporal analysis of properties expressed in Signal Spatio-Temporal Logic (SSTL), to give further insight into the dynamic behaviour of systems. Our novel analysis starts from the estimation of satisfaction probabilities of given SSTL properties and allows the analysis of their temporal and spatial evolution. Moreover, in our verification procedure, we use a three-valued approach to include the intrinsic and unavoidable uncertainty related to the simulation-based statistical evaluation of the estimates; this can be also used to assess the appropriate number of simulations to use depending on the analysis needs. We present the syntax and three-valued semantics of TSTL and a specific extended monitoring algorithm to check the validity of TSTL formulas. We conclude with two case studies that demonstrate how TSTL broadens the application of spatio-temporal logics in realistic scenarios, enabling analysis of threat monitoring and control programmes based on spatial stochastic population models.

Notes

Acknowledgement

This work was supported by Microsoft Research Cambridge through its PhD Scholarship Programme and by the EU project QUANTICOL 600708. Glenn Marion was funded by the Scottish Government Rural and Environment Science and Analytical Services Division (RESAS).

References

  1. 1.
    Legay, A., Delahaye, B., Bensalem, S.: Statistical model checking: an overview. In: Barringer, H., Falcone, Y., Finkbeiner, B., Havelund, K., Lee, I., Pace, G., Roşu, G., Sokolsky, O., Tillmann, N. (eds.) RV 2010. LNCS, vol. 6418, pp. 122–135. Springer, Heidelberg (2010). doi: 10.1007/978-3-642-16612-9_11 CrossRefGoogle Scholar
  2. 2.
    Nenzi, L., Bortolussi, L., Ciancia, V., Loreti, M., Massink, M.: Qualitative and quantitative monitoring of spatio-temporal properties. In: Bartocci, E., Majumdar, R. (eds.) RV 2015. LNCS, vol. 9333, pp. 21–37. Springer, Cham (2015). doi: 10.1007/978-3-319-23820-3_2 CrossRefGoogle Scholar
  3. 3.
    Aiello, M., Pratt-Hartmann, I., Van Benthem, J.: Handbook of Spatial Logics. Springer, Netherlands (2007)CrossRefzbMATHGoogle Scholar
  4. 4.
    Cardelli, L., Gordon, A.D.: Anytime, anywhere: modal logics for mobile ambients. In: POPL 2000, pp. 365–377. ACM (2000)Google Scholar
  5. 5.
    Reif, J., Sistla, A.: A multiprocess network logic with temporal and spatial modalities. J. Comput. Syst. Sci. 30(1), 41–53 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Hansson, H., Jonsson, B.: A logic for reasoning about time and reliability. Formal Aspects Comput. 6(5), 512–535 (1994)CrossRefzbMATHGoogle Scholar
  7. 7.
    Baier, C., Haverkort, B., Hermanns, H., Katoen, J.P.: Model-checking algorithms for continuous-time Markov chains. IEEE TSE 29, 524–541 (2003)zbMATHGoogle Scholar
  8. 8.
    Gottwald, S.: Many-valued logic. In: Stanford Encyclopedia of Philosophy (2008)Google Scholar
  9. 9.
    Łukasiewicz, J.: Selected Works. North-Holland Publishing Company, Amsterdam (1970)zbMATHGoogle Scholar
  10. 10.
    Kleene, S.C.: On notation for ordinal numbers. JSL 3(4), 150–155 (1938)zbMATHGoogle Scholar
  11. 11.
    Katoen, J.-P., Klink, D., Leucker, M., Wolf, V.: Three-valued abstraction for probabilistic systems. JLAP 81(4), 356–389 (2012)MathSciNetzbMATHGoogle Scholar
  12. 12.
    Sen, K., Viswanathan, M., Agha, G.: Model-checking Markov chains in the presence of uncertainties. In: Hermanns, H., Palsberg, J. (eds.) TACAS 2006. LNCS, vol. 3920, pp. 394–410. Springer, Heidelberg (2006). doi: 10.1007/11691372_26 CrossRefGoogle Scholar
  13. 13.
    Maler, O., Nickovic, D.: Monitoring temporal properties of continuous signals. In: Lakhnech, Y., Yovine, S. (eds.) FORMATS/FTRTFT -2004. LNCS, vol. 3253, pp. 152–166. Springer, Heidelberg (2004). doi: 10.1007/978-3-540-30206-3_12 CrossRefGoogle Scholar
  14. 14.
    Luisa Vissat, L., Hillston, J., Marion, G., Smith, M.J.: Mela: modelling in ecology with location attributes. In: EPTCS, vol. 227, pp. 82–97 (2016)Google Scholar
  15. 15.
    Gillespie, D.T.: Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 81(25), 2340–2361 (1977)CrossRefGoogle Scholar
  16. 16.
    Nenzi, L., Bortolussi, L., Loreti, M.: jSSTL - a tool to monitor spatio-temporal properties. ValueTools (2016)Google Scholar
  17. 17.
    Cerotti, D., Gribaudo, M., Bobbio, A., Calafate, C.T., Manzoni, P.: A Markovian agent model for fire propagation in outdoor environments. In: Aldini, A., Bernardo, M., Bononi, L., Cortellessa, V. (eds.) EPEW 2010. LNCS, vol. 6342, pp. 131–146. Springer, Heidelberg (2010). doi: 10.1007/978-3-642-15784-4_9 CrossRefGoogle Scholar
  18. 18.
    Baier, C., Haverkort, B., Hermanns, H., Katoen, J.-P.: On the logical characterisation of performability properties. In: Montanari, U., Rolim, J.D.P., Welzl, E. (eds.) ICALP 2000. LNCS, vol. 1853, pp. 780–792. Springer, Heidelberg (2000). doi: 10.1007/3-540-45022-X_65 CrossRefGoogle Scholar
  19. 19.
    Catterall, S., Cook, A.R., Marion, G., Butler, A., Hulme, P.E.: Accounting for uncertainty in colonisation times: a novel approach to modelling the spatio-temporal dynamics of alien invasions using distribution data. Ecography 35(10), 901–911 (2012)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Ludovica Luisa Vissat
    • 1
  • Michele Loreti
    • 2
  • Laura Nenzi
    • 3
  • Jane Hillston
    • 1
  • Glenn Marion
    • 4
  1. 1.School of InformaticsUniversity of EdinburghEdinburghUK
  2. 2.DiSIAUniversity of FirenzeFlorenceItaly
  3. 3.Faculty of InformaticsVienna University of TechnologyViennaAustria
  4. 4.Biomathematics and Statistics ScotlandEdinburghUK

Personalised recommendations