Online Causation Monitoring of Signal Temporal Logic

TL;DR

This paper introduces causation-based online monitoring methods for Signal Temporal Logic that provide more detailed insights into system behavior and violations, overcoming limitations of traditional robustness interval approaches.

Contribution

It proposes Boolean and quantitative causation monitors that enhance system evolution understanding without significantly increasing monitoring costs.

Findings

Causation monitors offer more detailed system evolution information.

Proposed monitors can be derived from classic robustness-based monitors.

Experimental results confirm improved insight with similar computational costs.

Abstract

Online monitoring is an effective validation approach for hybrid systems, that, at runtime, checks whether the (partial) signals of a system satisfy a specification in, e.g., Signal Temporal Logic (STL). The classic STL monitoring is performed by computing a robustness interval that specifies, at each instant, how far the monitored signals are from violating and satisfying the specification. However, since a robustness interval monotonically shrinks during monitoring, classic online monitors may fail in reporting new violations or in precisely describing the system evolution at the current instant. In this paper, we tackle these issues by considering the causation of violation or satisfaction, instead of directly using the robustness. We first introduce a Boolean causation monitor that decides whether each instant is relevant to the violation or satisfaction of the specification. We then extend this monitor to a quantitative causation monitor that tells how far an instant is from being relevant to the violation or satisfaction. We further show that classic monitors can be derived from our proposed ones. Experimental results show that the two proposed monitors are able to provide more detailed information about system evolution, without requiring a significantly higher monitoring cost.