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.
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Notes
- 1.
We need to take into account that a temporal formula looks \(T_f\) time units into the future, hence the domain [0, T] becomes \([0,T-T_f]\).
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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).
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Luisa Vissat, L., Loreti, M., Nenzi, L., Hillston, J., Marion, G. (2017). Three-Valued Spatio-Temporal Logic: A Further Analysis on Spatio-Temporal Properties of Stochastic Systems. In: Bertrand, N., Bortolussi, L. (eds) Quantitative Evaluation of Systems. QEST 2017. Lecture Notes in Computer Science(), vol 10503. Springer, Cham. https://doi.org/10.1007/978-3-319-66335-7_22
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