Incremental reasoning in probabilistic Signal Temporal Logic Abstract   Robot safety is of growing concern given recent developments in intelligent autonomous systems. For complex agents operating in uncertain, complex and rapidlychanging environments it is difficult to guarantee safety without imposing unrealistic assumptions and restrictions. It is therefore necessary to complement traditional formal verification with monitoring of the running system after deployment. Runtime verification can be used to monitor that an agent behaves according to a formal specification. The specification can contain safetyrelated requirements and assumptions about the environment, environmentagent interactions and agentagent interactions. A key problem is the uncertain and changing nature of the environment. This necessitates requirements on how probable a certain outcome is and on predictions of future states. We propose Probabilistic Signal Temporal Logic (ProbSTL) by extending Signal Temporal Logic with a sublanguage to allow statements over probabilities, observations and predictions. We further introduce and prove the correctness of the incremental stream reasoning technique progression over wellformed formulas in ProbSTL. Experimental evaluations demonstrate the applicability and benefits of ProbSTL for robot safety.

Optimal Temporal Logic Planning for MultiRobot Systems in Uncertain Semantic Maps This paper addresses a multirobot motion planning problem in probabilistic maps obtained by semantic simultaneous localization and mapping (SLAM). The goal of the robots is to accomplish complex collaborative high level tasks captured by global temporal logic specifications in the presence of uncertainty in the workspace. Specifically, the robots operate in an unknown environment modeled as a semantic map determined by Gaussian distributions over landmark positions and arbitrary discrete distributions over landmark classes. We extend Linear Temporal Logic by including informationbased predicates allowing us to incorporate uncertainty and probabilistic satisfaction requirements directly into the task specification. We propose a new highly scalable samplingbased approach that synthesizes paths that satisfy the assigned task specification while minimizing a userspecified motion cost function. Finally, we show that the proposed algorithm is probabilistically complete, asymptotically optimal and supported by convergence rate bounds. We provide extensive simulation results that corroborate the theoretical analysis and show that the proposed algorithm can address largescale planning tasks.