Quantitative Monitoring of Signal First-Order Logic

TL;DR

This paper introduces a novel quantitative semantics for Signal First-Order Logic (SFO), enabling real-time, robust monitoring of hybrid system signals with an efficient online algorithm and a practical prototype.

Contribution

It provides the first robustness-based quantitative semantics for SFO and develops an efficient online monitoring algorithm with a prototype implementation.

Findings

The past-time fragment enables online monitoring of SFO.

The monitoring algorithm is efficient and practical.

The prototype demonstrates real-world applicability.

Abstract

Runtime monitoring checks, during execution, whether a partial signal produced by a hybrid system satisfies its specification. Signal First-Order Logic (SFO) offers expressive real-time specifications over such signals, but currently comes only with Boolean semantics and has no tool support. We provide the first robustness-based quantitative semantics for SFO, enabling the expression and evaluation of rich real-time properties beyond the scope of existing formalisms such as Signal Temporal Logic. To enable online monitoring, we identify a past-time fragment of SFO and give a pastification procedure that transforms bounded-response SFO formulas into equisatisfiable formulas in this fragment. We then develop an efficient runtime monitoring algorithm for this past-time fragment and evaluate its performance on a set of benchmarks, demonstrating the practicality and effectiveness of our approach. To the best of our knowledge, this is the first publicly available prototype for online quantitative monitoring of full SFO.