{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,17]],"date-time":"2026-08-17T15:02:09Z","timestamp":1786978929742,"version":"build-2736575974"},"publisher-location":"Cham","reference-count":37,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783032060952","type":"print"},{"value":"9783032060969","type":"electronic"}],"license":[{"start":{"date-parts":[[2025,9,27]],"date-time":"2025-09-27T00:00:00Z","timestamp":1758931200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,9,27]],"date-time":"2025-09-27T00:00:00Z","timestamp":1758931200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026]]},"DOI":"10.1007\/978-3-032-06096-9_1","type":"book-chapter","created":{"date-parts":[[2025,9,26]],"date-time":"2025-09-26T09:54:20Z","timestamp":1758880460000},"page":"3-18","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Bridging Logic and\u00a0Learning: Decoding Temporal Logic Embeddings via\u00a0Transformers"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-5198-6970","authenticated-orcid":false,"given":"Sara","family":"Candussio","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-2948-7705","authenticated-orcid":false,"given":"Gaia","family":"Saveri","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8715-2987","authenticated-orcid":false,"given":"Gabriele","family":"Sarti","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8874-4001","authenticated-orcid":false,"given":"Luca","family":"Bortolussi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,9,27]]},"reference":[{"key":"1_CR1","doi-asserted-by":"crossref","unstructured":"Aydin, S.K., Gol, E.A.: Synthesis of monitoring rules with STL. J. Circ. Syst. Comput. 29(11), 2050177:1\u20132050177:26 (2020)","DOI":"10.1142\/S0218126620501777"},{"key":"1_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1007\/978-3-319-75632-5_5","volume-title":"Lectures on Runtime Verification","author":"E Bartocci","year":"2018","unstructured":"Bartocci, E., Deshmukh, J., Donz\u00e9, A., Fainekos, G., Maler, O., Ni\u010dkovi\u0107, D., Sankaranarayanan, S.: Specification-based monitoring of cyber-physical systems: a survey on theory, tools and Applications. In: Bartocci, E., Falcone, Y. (eds.) Lectures on Runtime Verification. LNCS, vol. 10457, pp. 135\u2013175. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-319-75632-5_5"},{"key":"1_CR3","doi-asserted-by":"crossref","unstructured":"Bartocci, E., Mateis, C., Nesterini, E., Nickovic, D.: Survey on mining signal temporal logic specifications. Inf. Comput. 289(Part), 104957 (2022)","DOI":"10.1016\/j.ic.2022.104957"},{"key":"1_CR4","doi-asserted-by":"crossref","unstructured":"Bombara, G., Vasile, C.I., Penedo, F., Yasuoka, H., Belta, C.: A decision tree approach to data classification using signal temporal logic. In: Proceedings of the 19th International Conference on Hybrid Systems: Computation and Control, HSCC 2016, pp. 1\u201310. ACM (2016)","DOI":"10.1145\/2883817.2883843"},{"key":"1_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1007\/978-3-030-99524-9_15","volume-title":"Tools and Algorithms for the Construction and Analysis of Systems","author":"L Bortolussi","year":"2022","unstructured":"Bortolussi, L., Gallo, G.M., K\u0159et\u00ednsk\u00fd, J., Nenzi, L.: Learning model checking and the kernel trick for signal temporal logic on stochastic processes. In: TACAS 2022. LNCS, vol. 13243, pp. 281\u2013300. Springer, Cham (2022). https:\/\/doi.org\/10.1007\/978-3-030-99524-9_15"},{"key":"1_CR6","doi-asserted-by":"publisher","unstructured":"Cosler, M., Hahn, C., Mendoza, D., Schmitt, F., Trippel, C.: nl2spec: interactively translating unstructured natural language to temporal logics with large language models. In: Enea, C., Lal, A. (eds.) Computer Aided Verification - 35th International Conference, CAV 2023, Paris, France, 17\u201322 July 2023, Proceedings, Part II. Lecture Notes in Computer Science, vol. 13965, pp. 383\u2013396. Springer, Heidelberg (2023). https:\/\/doi.org\/10.1007\/978-3-031-37703-7_18","DOI":"10.1007\/978-3-031-37703-7_18"},{"key":"1_CR7","unstructured":"Crouse, M., et al.: Improving graph neural network representations of logical formulae with subgraph pooling. CoRR arxiv:1911.06904 (2019)"},{"key":"1_CR8","unstructured":"d\u2019Ascoli, S., Becker, S., Schwaller, P., Mathis, A., Kilbertus, N.: Odeformer: symbolic regression of dynamical systems with transformers. In: The Twelfth International Conference on Learning Representations, ICLR 2024, Vienna, Austria, 7\u201311 May 2024. OpenReview.net (2024)"},{"key":"1_CR9","unstructured":"Hahn, C., Schmitt, F., Kreber, J.U., Rabe, M.N., Finkbeiner, B.: Teaching temporal logics to neural networks. In: 9th International Conference on Learning Representations, ICLR 2021, Virtual Event, Austria, 3\u20137 May 2021. OpenReview.net (2021)"},{"key":"1_CR10","unstructured":"Hahn, C., Schmitt, F., Tillman, J.J., Metzger, N., Siber, J., Finkbeiner, B.: Formal specifications from natural language. CoRR arxiv:2206.01962 (2022)"},{"issue":"2","key":"1_CR11","doi-asserted-by":"publisher","first-page":"5246","DOI":"10.1109\/LRA.2022.3155197","volume":"7","author":"W Hashimoto","year":"2022","unstructured":"Hashimoto, W., Hashimoto, K., Takai, S.: Stl2vec: signal temporal logic embeddings for control synthesis with recurrent neural networks. IEEE Rob. Autom. Lett. 7(2), 5246\u20135253 (2022)","journal-title":"IEEE Rob. Autom. Lett."},{"key":"1_CR12","doi-asserted-by":"crossref","unstructured":"He, J., Bartocci, E., Nickovic, D., Isakovic, H., Grosu, R.: Deepstl - from english requirements to signal temporal logic. In: 44th IEEE\/ACM 44th International Conference on Software Engineering, ICSE 2022, Pittsburgh, PA, USA, 25\u201327 May 2022, pp. 610\u2013622. ACM (2022)","DOI":"10.1145\/3510003.3510171"},{"key":"1_CR13","unstructured":"Hendrycks, D., Gimpel, K.: Gaussian error linear units (gelus) (2016). https:\/\/api.semanticscholar.org\/CorpusID:125617073"},{"key":"1_CR14","unstructured":"Isik, I., Gol, E.A., Cinbis, R.G.: Learning to estimate system specifications in linear temporal logic using transformers and mamba. CoRR arxiv:2405.20917 (2024)"},{"key":"1_CR15","unstructured":"Kamienny, P., d\u2019Ascoli, S., Lample, G., Charton, F.: End-to-end symbolic regression with transformers. In: Koyejo, S., Mohamed, S., Agarwal, A., Belgrave, D., Cho, K., Oh, A. (eds.) Advances in Neural Information Processing Systems 35: Annual Conference on Neural Information Processing Systems 2022, NeurIPS 2022, New Orleans, LA, USA, 28 November\u20139 December 2022 (2022)"},{"key":"1_CR16","doi-asserted-by":"publisher","unstructured":"Khandait, T., et al.: Arch-comp 2024 category report: falsification. In: Frehse, G., Althoff, M. (eds.) Proceedings of the 11th International Workshop on Applied Verification for Continuous and Hybrid Systems. EPiC Series in Computing, vol.\u00a0103, pp. 122\u2013144. EasyChair (2024). https:\/\/doi.org\/10.29007\/hgfv. https:\/\/easychair.org\/publications\/paper\/fKVR","DOI":"10.29007\/hgfv"},{"issue":"4","key":"1_CR17","doi-asserted-by":"publisher","first-page":"3563","DOI":"10.1109\/TKDE.2021.3139333","volume":"35","author":"Q Lin","year":"2023","unstructured":"Lin, Q., et al.: Contrastive graph representations for logical formulas embedding. IEEE Trans. Knowl. Data Eng. 35(4), 3563\u20133574 (2023)","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"1_CR18","unstructured":"Loshchilov, I., Hutter, F.: Decoupled weight decay regularization (2019). https:\/\/arxiv.org\/abs\/1711.05101"},{"key":"1_CR19","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"152","DOI":"10.1007\/978-3-540-30206-3_12","volume-title":"Formal Techniques, Modelling and Analysis of Timed and Fault-Tolerant Systems","author":"O Maler","year":"2004","unstructured":"Maler, O., Nickovic, D.: Monitoring temporal properties of continuous signals. In: Lakhnech, Y., Yovine, S. (eds.) FORMATS\/FTRTFT -2004. LNCS, vol. 3253, pp. 152\u2013166. Springer, Heidelberg (2004). https:\/\/doi.org\/10.1007\/978-3-540-30206-3_12"},{"key":"1_CR20","doi-asserted-by":"crossref","unstructured":"Mohammadinejad, S., Deshmukh, J.V., Puranic, A.G., Vazquez-Chanlatte, M., Donz\u00e9, A.: Interpretable classification of time-series data using efficient enumerative techniques. In: HSCC \u201920: 23rd ACM International Conference on Hybrid Systems: Computation and Control, pp. 9:1\u20139:10. ACM (2020)","DOI":"10.1145\/3365365.3382218"},{"key":"1_CR21","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1007\/978-3-319-99154-2_20","volume-title":"Quantitative Evaluation of Systems","author":"L Nenzi","year":"2018","unstructured":"Nenzi, L., Silvetti, S., Bartocci, E., Bortolussi, L.: A robust genetic algorithm for learning temporal specifications from data. In: McIver, A., Horvath, A. (eds.) QEST 2018. LNCS, vol. 11024, pp. 323\u2013338. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-319-99154-2_20"},{"key":"1_CR22","doi-asserted-by":"crossref","unstructured":"Norheim, J.J., Rebentisch, E., Xiao, D., Draeger, L., Kerbrat, A., de\u00a0Weck, O.L.: Challenges in applying large language models to requirements engineering tasks. Des. Sci. 10 (2024)","DOI":"10.1017\/dsj.2024.8"},{"key":"1_CR23","doi-asserted-by":"crossref","unstructured":"Pnueli, A.: The temporal logic of programs. In: 18th Annual Symposium on Foundations of Computer Science (sfcs 1977), pp. 46\u201357 (1977)","DOI":"10.1109\/SFCS.1977.32"},{"key":"1_CR24","unstructured":"Qin, T., Saphra, N., Alvarez-Melis, D.: Sometimes i am a tree: data drives fragile hierarchical generalization. In: NeurIPS 2024 Workshop on Scientific Methods for Understanding Deep Learning (2024). https:\/\/openreview.net\/forum?id=AHakCjAPOh"},{"key":"1_CR25","unstructured":"Radford, A., Narasimhan, K., Salimans, T., Sutskever, I.: Improving language understanding by generative pre-training. OpenAI Blog (2018). https:\/\/cdn.openai.com\/research-covers\/language-unsupervised\/language_understanding_paper.pdf"},{"key":"1_CR26","doi-asserted-by":"crossref","unstructured":"Saglam, I., Gol, E.A.: Cause mining and controller synthesis with STL. In: 58th IEEE Conference on Decision and Control, CDC 2019, pp. 4589\u20134594. IEEE (2019)","DOI":"10.1109\/CDC40024.2019.9029894"},{"key":"1_CR27","doi-asserted-by":"publisher","unstructured":"Saveri, G., Bortolussi, L.: Retrieval-augmented mining of temporal logic specifications from data. In: Machine Learning and Knowledge Discovery in Databases. Research Track - European Conference, ECML PKDD 2024, Vilnius, Lithuania, 9\u201313 September 2024, Proceedings, Part VII. Lecture Notes in Computer Science, vol. 14947, pp. 315\u2013331. Springer, Heidelberg (2024). https:\/\/doi.org\/10.1007\/978-3-031-70368-3_19","DOI":"10.1007\/978-3-031-70368-3_19"},{"key":"1_CR28","doi-asserted-by":"crossref","unstructured":"Saveri, G., Nenzi, L., Bortolussi, L., Kret\u00ednsk\u00fd, J.: stl2vec: Semantic and interpretable vector representation of temporal logic. In: 27th European Conference on Artificial Intelligence, Santiago de Compostela, Spain, 19\u201324 October 2024. Frontiers in Artificial Intelligence and Applications, vol.\u00a0392, pp. 1381 \u2013 1388. IOS Press (2024)","DOI":"10.3233\/FAIA240638"},{"key":"1_CR29","unstructured":"Shojaee, P., Meidani, K., Farimani, A.B., Reddy, C.K.: Transformer-based planning for symbolic regression. In: Oh, A., Naumann, T., Globerson, A., Saenko, K., Hardt, M., Levine, S. (eds.) Advances in Neural Information Processing Systems 36: Annual Conference on Neural Information Processing Systems 2023, NeurIPS 2023, New Orleans, LA, USA, 10\u201316 December 2023 (2023)"},{"issue":"5","key":"1_CR30","doi-asserted-by":"publisher","first-page":"3250","DOI":"10.1109\/TIT.2011.2182033","volume":"58","author":"N Srinivas","year":"2012","unstructured":"Srinivas, N., Krause, A., Kakade, S.M., Seeger, M.W.: Information-theoretic regret bounds for gaussian process optimization in the bandit setting. IEEE Trans. Inf. Theory 58(5), 3250\u20133265 (2012)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"1_CR31","doi-asserted-by":"crossref","unstructured":"Vaidyanathan, P., et al.: Grid-based temporal logic inference. In: 56th IEEE Annual Conference on Decision and Control, CDC 2017, pp. 5354\u20135359. IEEE (2017)","DOI":"10.1109\/CDC.2017.8264452"},{"key":"1_CR32","unstructured":"Vaswani, A., et al.: Attention is all you need. In: Advances in Neural Information Processing Systems 30: Annual Conference on Neural Information Processing Systems, pp. 5998\u20136008 (2017)"},{"key":"1_CR33","unstructured":"Xie, Y., Xu, Z., Meel, K.S., Kankanhalli, M.S., Soh, H.: Embedding symbolic knowledge into deep networks. In: NeurIPS 2019, Vancouver, BC, Canada, 8\u201314 December 2019, pp. 4235\u20134245 (2019)"},{"key":"1_CR34","unstructured":"Yenduri, G., et al.: Generative pre-trained transformer: a comprehensive review on enabling technologies, potential applications, emerging challenges, and future directions (2023). https:\/\/arxiv.org\/abs\/2305.10435"},{"key":"1_CR35","unstructured":"Zhao, W.X., et al.: A survey of large language models. CoRR arxiv:2303.18223 (2025)"},{"key":"1_CR36","doi-asserted-by":"crossref","unstructured":"d\u2019A Garcez, A., Lamb, L.C.: Neurosymbolic AI: the 3rd wave. Artif. Intell. Rev. 56(11) (2023)","DOI":"10.1007\/s10462-023-10448-w"},{"key":"1_CR37","doi-asserted-by":"publisher","DOI":"10.1016\/j.artint.2023.104062","volume":"328","author":"G Marra","year":"2024","unstructured":"Marra, G., Manhaeve, R., Tiddi, I., De Raedt, L.: From statistical relational to neurosymbolic artificial intelligence: a survey. Artif. Intell. 328, 104062 (2024)","journal-title":"Artif. Intell."}],"container-title":["Lecture Notes in Computer Science","Machine Learning and Knowledge Discovery in Databases. Research Track"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-032-06096-9_1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T10:25:23Z","timestamp":1777631123000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-032-06096-9_1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,9,27]]},"ISBN":["9783032060952","9783032060969"],"references-count":37,"URL":"https:\/\/doi.org\/10.1007\/978-3-032-06096-9_1","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,9,27]]},"assertion":[{"value":"27 September 2025","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"The authors have no competing interests to declare that\u00a0are relevant to the content of this article.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Disclosure of Interests"}},{"value":"ECML PKDD","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Joint European Conference on Machine Learning and Knowledge Discovery in Databases","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Porto","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Portugal","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2025","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"15 September 2025","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"19 September 2025","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"ecml2025","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/ecmlpkdd.org\/2025\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}