[{"date_created":"2026-06-14T22:01:44Z","arxiv":1,"alternative_title":["LNCS"],"department":[{"_id":"ToHe"}],"date_updated":"2026-06-22T08:21:09Z","year":"2026","_id":"22006","quality_controlled":"1","abstract":[{"lang":"eng","text":"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."}],"acknowledgement":"We thank the anonymous reviewers for their helpful comments. This work was supported by the European Research Council (ERC) Grants VAMOS (No. 101020093) and HYPER (No. 101055412), and by the Advanced Research and Invention Agency under the Safeguarded AI programme (MSAI-PR01-P047).","publication_identifier":{"eissn":["1611-3349"],"issn":["0302-9743"],"isbn":["9783032262196"]},"OA_type":"hybrid","citation":{"chicago":"Chalupa, Marek, Thomas A Henzinger, Naci E Sarac, and Emily Yu. “Quantitative Monitoring of Signal First-Order Logic.” In <i>27th International Symposium on Formal Methods</i>, 16557:214–33. Springer Nature, 2026. <a href=\"https://doi.org/10.1007/978-3-032-26220-2_11\">https://doi.org/10.1007/978-3-032-26220-2_11</a>.","ieee":"M. Chalupa, T. A. Henzinger, N. E. Sarac, and E. Yu, “Quantitative monitoring of Signal First-Order logic,” in <i>27th International Symposium on Formal Methods</i>, Tokyo, Japan, 2026, vol. 16557, pp. 214–233.","apa":"Chalupa, M., Henzinger, T. A., Sarac, N. E., &#38; Yu, E. (2026). Quantitative monitoring of Signal First-Order logic. In <i>27th International Symposium on Formal Methods</i> (Vol. 16557, pp. 214–233). Tokyo, Japan: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-032-26220-2_11\">https://doi.org/10.1007/978-3-032-26220-2_11</a>","short":"M. Chalupa, T.A. Henzinger, N.E. Sarac, E. Yu, in:, 27th International Symposium on Formal Methods, Springer Nature, 2026, pp. 214–233.","ista":"Chalupa M, Henzinger TA, Sarac NE, Yu E. 2026. Quantitative monitoring of Signal First-Order logic. 27th International Symposium on Formal Methods. FM: Formal Methods, LNCS, vol. 16557, 214–233.","ama":"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>","mla":"Chalupa, Marek, et al. “Quantitative Monitoring of Signal First-Order Logic.” <i>27th International Symposium on Formal Methods</i>, vol. 16557, Springer Nature, 2026, pp. 214–33, doi:<a href=\"https://doi.org/10.1007/978-3-032-26220-2_11\">10.1007/978-3-032-26220-2_11</a>."},"article_processing_charge":"No","das_tickbox":"0","OA_place":"publisher","day":"18","oa_version":"Published Version","oa":1,"keyword":["Signal first-order logic","Robustness-based quantitative semantics","Online runtime monitoring"],"volume":16557,"ddc":["000"],"page":"214-233","publication_status":"published","tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"license":"https://creativecommons.org/licenses/by/4.0/","status":"public","intvolume":"     16557","title":"Quantitative monitoring of Signal First-Order logic","publisher":"Springer Nature","date_published":"2026-05-18T00:00:00Z","ec_funded":1,"author":[{"last_name":"Chalupa","full_name":"Chalupa, Marek","first_name":"Marek","id":"87e34708-d6c6-11ec-9f5b-9391e7be2463"},{"id":"40876CD8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2985-7724","last_name":"Henzinger","first_name":"Thomas A","full_name":"Henzinger, Thomas A"},{"id":"8C6B42F8-C8E6-11E9-A03A-F2DCE5697425","last_name":"Sarac","first_name":"Naci E","full_name":"Sarac, Naci E"},{"orcid":"0000-0002-4993-773X","id":"20aa2ae8-f2f1-11ed-bbfa-8205053f1342","first_name":"Zhengqi","full_name":"Yu, Zhengqi","last_name":"Yu"}],"language":[{"iso":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","scopus_import":"1","project":[{"name":"Vigilant Algorithmic Monitoring of Software","_id":"62781420-2b32-11ec-9570-8d9b63373d4d","grant_number":"101020093","call_identifier":"H2020"}],"month":"05","has_accepted_license":"1","type":"conference","conference":{"start_date":"2026-05-18","end_date":"2026-05-22","location":"Tokyo, Japan","name":"FM: Formal Methods"},"file":[{"checksum":"7055199ecb985e9e2e272f4988827067","content_type":"application/pdf","relation":"main_file","success":1,"file_name":"2026_LNCS_Chalupa.pdf","file_size":849237,"date_updated":"2026-06-22T08:18:41Z","access_level":"open_access","file_id":"22113","creator":"dernst","date_created":"2026-06-22T08:18:41Z"}],"file_date_updated":"2026-06-22T08:18:41Z","external_id":{"arxiv":["2603.00728"]},"doi":"10.1007/978-3-032-26220-2_11","publication":"27th International Symposium on Formal Methods"}]