{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T21:10:51Z","timestamp":1776373851454,"version":"3.51.2"},"publisher-location":"Cham","reference-count":28,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783031388279","type":"print"},{"value":"9783031388286","type":"electronic"}],"license":[{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"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":[[2023]]},"DOI":"10.1007\/978-3-031-38828-6_4","type":"book-chapter","created":{"date-parts":[[2023,7,19]],"date-time":"2023-07-19T12:05:32Z","timestamp":1689768332000},"page":"51-67","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Certified Logic-Based Explainable AI \u2013 The Case of\u00a0Monotonic Classifiers"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3266-6080","authenticated-orcid":false,"given":"Aur\u00e9lie","family":"Hurault","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6632-3086","authenticated-orcid":false,"given":"Joao","family":"Marques-Silva","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,7,20]]},"reference":[{"key":"4_CR1","doi-asserted-by":"crossref","unstructured":"Audemard, G., Koriche, F., Marquis, P.: On tractable XAI queries based on compiled representations. In: KR, pp. 838\u2013849 (2020)","DOI":"10.24963\/kr.2020\/86"},{"key":"4_CR2","doi-asserted-by":"publisher","unstructured":"Biere, A., Heule, M., van Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability - Second Edition, Frontiers in Artificial Intelligence and Applications, vol. 336. IOS Press (2021). https:\/\/doi.org\/10.3233\/FAIA336","DOI":"10.3233\/FAIA336"},{"key":"4_CR3","doi-asserted-by":"publisher","unstructured":"Chen, T., Guestrin, C.: XGBoost: a scalable tree boosting system. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD \u201916), pp. 785\u2013794. ACM, New York (2016). https:\/\/doi.org\/10.1145\/2939672.2939785","DOI":"10.1145\/2939672.2939785"},{"issue":"3","key":"4_CR4","doi-asserted-by":"publisher","first-page":"695","DOI":"10.1007\/s10817-018-9490-4","volume":"63","author":"L Cruz-Filipe","year":"2018","unstructured":"Cruz-Filipe, L., Marques-Silva, J., Schneider-Kamp, P.: Formally verifying the solution to the Boolean pythagorean triples problem. J. Automat. Reason. 63(3), 695\u2013722 (2018). https:\/\/doi.org\/10.1007\/s10817-018-9490-4","journal-title":"J. Automat. Reason."},{"issue":"6","key":"4_CR5","doi-asserted-by":"publisher","first-page":"906","DOI":"10.1109\/TNN.2010.2044803","volume":"21","author":"H Daniels","year":"2010","unstructured":"Daniels, H., Velikova, M.: Monotone and partially monotone neural networks. IEEE Trans. Neural Netw. 21(6), 906\u2013917 (2010)","journal-title":"IEEE Trans. Neural Netw."},{"key":"4_CR6","doi-asserted-by":"crossref","unstructured":"Guidotti, R., Monreale, A., Ruggieri, S., Turini, F., Giannotti, F., Pedreschi, D.: A survey of methods for explaining black box models. ACM Comput. Surv. 51(5), 93:1\u201393:42 (2019)","DOI":"10.1145\/3236009"},{"key":"4_CR7","unstructured":"Gunning, D.: Explainable artificial intelligence (xai). dARPA-BAA-16-53 (2016). https:\/\/www.darpa.mil\/attachments\/DARPA-BAA-16-53.pdf"},{"key":"4_CR8","doi-asserted-by":"publisher","unstructured":"Gunning, D., Aha, D.W.: Darpa\u2019s explainable artificial intelligence (XAI) program. AI Mag. 40(2), 44\u201358 (2019). https:\/\/doi.org\/10.1609\/aimag.v40i2.2850","DOI":"10.1609\/aimag.v40i2.2850"},{"key":"4_CR9","doi-asserted-by":"publisher","unstructured":"Gunning, D., Stefik, M., Choi, J., Miller, T., Stumpf, S., Yang, G.: XAI - explainable artificial intelligence. Sci. Robot. 4(37) (2019). https:\/\/doi.org\/10.1126\/scirobotics.aay7120","DOI":"10.1126\/scirobotics.aay7120"},{"key":"4_CR10","unstructured":"Huang, X., Marques-Silva, J.: The inadequacy of shapley values for explainability. arXiv preprint CoRR abs\/2302.08160 (2023). arXiv:2302.08160"},{"key":"4_CR11","doi-asserted-by":"crossref","unstructured":"Ignatiev, A.: Towards trustable explainable AI. In: IJCAI, pp. 5154\u20135158 (2020)","DOI":"10.24963\/ijcai.2020\/726"},{"key":"4_CR12","doi-asserted-by":"crossref","unstructured":"Ignatiev, A., Narodytska, N., Asher, N., Marques-Silva, J.: From contrastive to abductive explanations and back again. In: AIxIA, pp. 335\u2013355 (2020)","DOI":"10.1007\/978-3-030-77091-4_21"},{"key":"4_CR13","doi-asserted-by":"crossref","unstructured":"Ignatiev, A., Narodytska, N., Marques-Silva, J.: Abduction-based explanations for machine learning models. In: AAAI, pp. 1511\u20131519 (2019)","DOI":"10.1609\/aaai.v33i01.33011511"},{"key":"4_CR14","unstructured":"Ignatiev, A., Narodytska, N., Marques-Silva, J.: On validating, repairing and refining heuristic ML explanations. CoRR abs\/1907.02509 arXiv preprint (2019) arXiv:1907.02509"},{"key":"4_CR15","unstructured":"Liu, X., Han, X., Zhang, N., Liu, Q.: Certified monotonic neural networks. Adv. Neural Inf. Process. Syst. 33 (2020)"},{"key":"4_CR16","unstructured":"Lundberg, S.M., Lee, S.: A unified approach to interpreting model predictions. In: NeurIPS, pp. 4765\u20134774 (2017)"},{"key":"4_CR17","unstructured":"Marques-Silva, J.: Logic-based explainability in machine learning. CoRR abs\/2211.00541 arXiv preprint (2022). arXiv:2211.00541"},{"key":"4_CR18","unstructured":"Marques-Silva, J., Gerspacher, T., Cooper, M.C., Ignatiev, A., Narodytska, N.: Explanations for monotonic classifiers. In: ICML, pp. 7469\u20137479 (2021)"},{"key":"4_CR19","doi-asserted-by":"crossref","unstructured":"Marques-Silva, J., Ignatiev, A.: Delivering trustworthy AI through formal XAI. In: AAAI, pp. 12342\u201312350 (2022)","DOI":"10.1609\/aaai.v36i11.21499"},{"key":"4_CR20","doi-asserted-by":"publisher","unstructured":"Marques-Silva, J., Janota, M., Menc\u00eda, C.: Minimal sets on propositional formulae, problems and reductions. Artif. Intell. 252, 22\u201350 (2017). https:\/\/doi.org\/10.1016\/j.artint.2017.07.005","DOI":"10.1016\/j.artint.2017.07.005"},{"key":"4_CR21","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.artint.2018.07.007","volume":"267","author":"T Miller","year":"2019","unstructured":"Miller, T.: Explanation in artificial intelligence: insights from the social sciences. Artif. Intell. 267, 1\u201338 (2019)","journal-title":"Artif. Intell."},{"issue":"1","key":"4_CR22","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1016\/0004-3702(87)90062-2","volume":"32","author":"R Reiter","year":"1987","unstructured":"Reiter, R.: A theory of diagnosis from first principles. Artif. Intell. 32(1), 57\u201395 (1987)","journal-title":"Artif. Intell."},{"key":"4_CR23","doi-asserted-by":"crossref","unstructured":"Ribeiro, M.T., Singh, S., Guestrin, C.: \u201cWhy should I trust you?\": Explaining the predictions of any classifier. In: KDD, pp. 1135\u20131144 (2016)","DOI":"10.1145\/2939672.2939778"},{"key":"4_CR24","doi-asserted-by":"crossref","unstructured":"Ribeiro, M.T., Singh, S., Guestrin, C.: Anchors: high-precision model-agnostic explanations. In: AAAI, pp. 1527\u20131535 (2018)","DOI":"10.1609\/aaai.v32i1.11491"},{"key":"4_CR25","doi-asserted-by":"publisher","unstructured":"Seshia, S.A., Sadigh, D., Sastry, S.S.: Toward verified artificial intelligence. Commun. ACM 65(7), 46\u201355 (2022). https:\/\/doi.org\/10.1145\/3503914","DOI":"10.1145\/3503914"},{"key":"4_CR26","doi-asserted-by":"crossref","unstructured":"Shih, A., Choi, A., Darwiche, A.: A symbolic approach to explaining Bayesian network classifiers. In: IJCAI, pp. 5103\u20135111 (2018)","DOI":"10.24963\/ijcai.2018\/708"},{"key":"4_CR27","unstructured":"Sivaraman, A., Farnadi, G., Millstein, T.D., den Broeck, G.V.: Counterexample-guided learning of monotonic neural networks. In: Larochelle, H., Ranzato, M., Hadsell, R., Balcan, M., Lin, H. (eds.) Advances in Neural Information Processing Systems 33: Annual Conference on Neural Information Processing Systems 2020, NeurIPS 2020 (December), pp. 6\u201312. Virtual (2020). https:\/\/proceedings.neurips.cc\/paper\/2020\/hash\/8ab70731b1553f17c11a3bbc87e0b605-Abstract.html"},{"key":"4_CR28","unstructured":"You, S., Ding, D., Canini, K.R., Pfeifer, J., Gupta, M.R.: Deep lattice networks and partial monotonic functions. In: Guyon, I., et al. (eds.) Advances in Neural Information Processing Systems 30: Annual Conference on Neural Information Processing Systems 2017 (December), pp. 4\u20139, 2017. Long Beach, CA, USA, pp. 2981\u20132989 (2017), https:\/\/proceedings.neurips.cc\/paper\/2017\/hash\/464d828b85b0bed98e80ade0a5c43b0f-Abstract.html"}],"container-title":["Lecture Notes in Computer Science","Tests and Proofs"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-38828-6_4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,13]],"date-time":"2024-03-13T15:42:35Z","timestamp":1710344555000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-38828-6_4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023]]},"ISBN":["9783031388279","9783031388286"],"references-count":28,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-38828-6_4","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023]]},"assertion":[{"value":"20 July 2023","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"TAP","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Tests and Proofs","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Leicester","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"United Kingdom","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2023","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"18 July 2023","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"19 July 2023","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"17","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"tap2023","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/conf.researchr.org\/home\/tap-2023","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Single-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Easychair","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"14","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"8","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"2","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"57% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"2","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Yes","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}}]}}