pacSTL: PAC-Bounded Signal Temporal Logic from Data-Driven Reachability Analysis

Abstract:Signal Temporal Logic (STL) is an expressive language for specifying behaviors of dynamical systems from continuous signals. However, a limitation of standard STL is its inherently deterministic semantics, which prevents it from accommodating uncertainty. Existing approaches to overcome this limitation are computationally costly and limit real-time capability, requiring repeated trajectory sampling or the redesign of probability distributions over atomic propositions whenever the atomic propositions or specifications change. We introduce pacSTL, a framework that combines Probably Approximately Correct (PAC)-bounded reachable set predictions with an interval extension of STL. pacSTL computes lower and upper bounds on atomic robustness values by solving optimization problems over PAC-bounded reachable sets and propagates the bounds through the temporal logic operators. The resulting evaluation yields a PAC-bounded robustness interval at the specification level. We demonstrate the efficiency and relevance of pacSTL by verifying a quadrotor flight scenario and runtime monitoring a maritime navigation specification.

Logic in Computer Science (cs.LO); Robotics (cs.RO)

arXiv:2511.00934 [cs.LO]

(or arXiv:2511.00934v2 [cs.LO] for this version)

https://doi.org/10.48550/arXiv.2511.00934 Focus to learn more arXiv-issued DOI via DataCite

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