TY - GEN
T1 - Uncertainty-Aware Signal Temporal Logic Inference
AU - Baharisangari, Nasim
AU - Gaglione, Jean Raphaël
AU - Neider, Daniel
AU - Topcu, Ufuk
AU - Xu, Zhe
N1 - Funding Information:
Acknowledgment. The authors thank Dr. Rebecca Russell and the entire ALPACA team for their collaboration. This material is based upon work supported by the Defense Advanced Research Projects Agency (DARPA) under Contract No. HR001120C0032.
Publisher Copyright:
© 2022, Springer Nature Switzerland AG.
PY - 2022
Y1 - 2022
N2 - Temporal logic inference is the process of extracting formal descriptions of system behaviors from data in the form of temporal logic formulas. The existing temporal logic inference methods mostly neglect uncertainties in the data, which results in the limited applicability of such methods in real-world deployments. In this paper, we first investigate the uncertainties associated with trajectories of a system and represent such uncertainties in the form of interval trajectories. We then propose two uncertainty-aware signal temporal logic (STL) inference approaches to classify the undesired behaviors and desired behaviors of a system. Instead of classifying finitely many trajectories, we classify infinitely many trajectories within the interval trajectories. In the first approach, we incorporate robust semantics of STL formulas with respect to an interval trajectory to quantify the margin at which an STL formula is satisfied or violated by the interval trajectory. The second approach relies on the first learning algorithm and exploits the decision trees to infer STL formulas to classify behaviors of a given system. The proposed approaches also work for non-separable data by optimizing the worst-case robustness margin in inferring an STL formula. Finally, we evaluate the performance of the proposed algorithms and present the obtained numerical results, where the proposed algorithms show reduction in the computation time by up to the factor of 95 on average, while the worst-case robustness margins are improved by up to 330% in comparison with the sampling-based baseline algorithms.
AB - Temporal logic inference is the process of extracting formal descriptions of system behaviors from data in the form of temporal logic formulas. The existing temporal logic inference methods mostly neglect uncertainties in the data, which results in the limited applicability of such methods in real-world deployments. In this paper, we first investigate the uncertainties associated with trajectories of a system and represent such uncertainties in the form of interval trajectories. We then propose two uncertainty-aware signal temporal logic (STL) inference approaches to classify the undesired behaviors and desired behaviors of a system. Instead of classifying finitely many trajectories, we classify infinitely many trajectories within the interval trajectories. In the first approach, we incorporate robust semantics of STL formulas with respect to an interval trajectory to quantify the margin at which an STL formula is satisfied or violated by the interval trajectory. The second approach relies on the first learning algorithm and exploits the decision trees to infer STL formulas to classify behaviors of a given system. The proposed approaches also work for non-separable data by optimizing the worst-case robustness margin in inferring an STL formula. Finally, we evaluate the performance of the proposed algorithms and present the obtained numerical results, where the proposed algorithms show reduction in the computation time by up to the factor of 95 on average, while the worst-case robustness margins are improved by up to 330% in comparison with the sampling-based baseline algorithms.
KW - Decision trees
KW - Temporal logic inference
KW - Uncertainties
UR - http://www.scopus.com/inward/record.url?scp=85126224053&partnerID=8YFLogxK
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U2 - 10.1007/978-3-030-95561-8_5
DO - 10.1007/978-3-030-95561-8_5
M3 - Conference contribution
AN - SCOPUS:85126224053
SN - 9783030955601
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 61
EP - 85
BT - Software Verification - 13th International Conference, VSTTE 2021 and 14th International Workshop, NSV 2021, Revised Selected Papers
A2 - Bloem, Roderick
A2 - Dimitrova, Rayna
A2 - Fan, Chuchu
A2 - Sharygina, Natasha
PB - Springer Science and Business Media Deutschland GmbH
T2 - 13th International Conference on Verified Software: Theories, Tools, and Experiments, VSTTE 2021 and 14th International Workshop on Numerical Software Verification, NSV 2021
Y2 - 18 October 2021 through 19 October 2021
ER -