Quantitative monitoring of Signal First-Order logic LNCS Chalupa, Marek Henzinger, Thomas A ; https://orcid.org/0000-0002-2985-7724 Sarac, Naci E Yu, Zhengqi ; https://orcid.org/0000-0002-4993-773X Signal first-order logic Robustness-based quantitative semantics Online runtime monitoring ddc:000 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. Springer Nature 2026 info:eu-repo/semantics/conferenceObject doc-type:conferenceObject text http://purl.org/coar/resource_type/c_5794 https://research-explorer.ista.ac.at/record/22006 https://research-explorer.ista.ac.at/download/22006/22113 Chalupa M, Henzinger TA, Sarac NE, Yu E. Quantitative monitoring of Signal First-Order logic. In: <i>27th International Symposium on Formal Methods</i>. Vol 16557. Springer Nature; 2026:214-233. doi:<a href="https://doi.org/10.1007/978-3-032-26220-2_11">10.1007/978-3-032-26220-2_11</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1007/978-3-032-26220-2_11 info:eu-repo/semantics/altIdentifier/issn/0302-9743 info:eu-repo/semantics/altIdentifier/e-issn/1611-3349 info:eu-repo/semantics/altIdentifier/isbn/9783032262196 info:eu-repo/semantics/altIdentifier/arxiv/2603.00728 info:eu-repo/semantics/openAccess