{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,11,23]],"date-time":"2024-11-23T19:40:29Z","timestamp":1732390829340,"version":"3.28.0"},"publisher-location":"Cham","reference-count":93,"publisher":"Springer Nature Switzerland","isbn-type":[{"type":"print","value":"9783031637995"},{"type":"electronic","value":"9783031638008"}],"license":[{"start":{"date-parts":[[2024,1,1]],"date-time":"2024-01-01T00:00:00Z","timestamp":1704067200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,1,1]],"date-time":"2024-01-01T00:00:00Z","timestamp":1704067200000},"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":[[2024]]},"DOI":"10.1007\/978-3-031-63800-8_10","type":"book-chapter","created":{"date-parts":[[2024,7,9]],"date-time":"2024-07-09T23:03:55Z","timestamp":1720566235000},"page":"185-206","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Categorical Foundation of\u00a0Explainable AI: A Unifying Theory"],"prefix":"10.1007","author":[{"ORCID":"http:\/\/orcid.org\/0000-0001-8492-8110","authenticated-orcid":false,"given":"Francesco","family":"Giannini","sequence":"first","affiliation":[]},{"ORCID":"http:\/\/orcid.org\/0000-0001-6918-1805","authenticated-orcid":false,"given":"Stefano","family":"Fioravanti","sequence":"additional","affiliation":[]},{"ORCID":"http:\/\/orcid.org\/0000-0003-3155-2564","authenticated-orcid":false,"given":"Pietro","family":"Barbiero","sequence":"additional","affiliation":[]},{"ORCID":"http:\/\/orcid.org\/0000-0001-5895-4809","authenticated-orcid":false,"given":"Alberto","family":"Tonda","sequence":"additional","affiliation":[]},{"ORCID":"http:\/\/orcid.org\/0000-0002-0540-5053","authenticated-orcid":false,"given":"Pietro","family":"Li\u00f2","sequence":"additional","affiliation":[]},{"ORCID":"http:\/\/orcid.org\/0000-0002-7783-5079","authenticated-orcid":false,"given":"Elena","family":"Di Lavore","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,7,10]]},"reference":[{"key":"10_CR1","doi-asserted-by":"crossref","unstructured":"Abramsky, S., Coecke, B.: A categorical semantics of quantum protocols. In: Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, pp. 415\u2013425 (2004)","DOI":"10.1109\/LICS.2004.1319636"},{"key":"10_CR2","doi-asserted-by":"publisher","first-page":"52138","DOI":"10.1109\/ACCESS.2018.2870052","volume":"6","author":"A Adadi","year":"2018","unstructured":"Adadi, A., Berrada, M.: Peeking inside the black-box: a survey on explainable artificial intelligence (xai). IEEE Access 6, 52138\u201352160 (2018)","journal-title":"IEEE Access"},{"key":"10_CR3","unstructured":"Aguinaldo, A., Regli, W.: A graphical model-based representation for classical ai plans using category theory. In: ICAPS 2021 Workshop on Explainable AI Planning (2021)"},{"key":"10_CR4","doi-asserted-by":"publisher","first-page":"82","DOI":"10.1016\/j.inffus.2019.12.012","volume":"58","author":"AB Arrieta","year":"2020","unstructured":"Arrieta, A.B., et al.: Explainable artificial intelligence (XAI): concepts, taxonomies, opportunities and challenges toward responsible AI. Inf. Fusion 58, 82\u2013115 (2020)","journal-title":"Inf. Fusion"},{"key":"10_CR5","unstructured":"Barbiero, P., et al.: Interpretable neural-symbolic concept reasoning. In: Krause, A., Brunskill, E., Cho, K., Engelhardt, B., Sabato, S., Scarlett, J. (eds.) Proceedings of the 40th International Conference on Machine Learning. Proceedings of Machine Learning Research, vol.\u00a0202, pp. 1801\u20131825. PMLR (2023). https:\/\/proceedings.mlr.press\/v202\/barbiero23a.html"},{"key":"10_CR6","volume-title":"Classification and regression trees","author":"L Breiman","year":"1984","unstructured":"Breiman, L., Friedman, J., Stone, C.J., Olshen, R.A.: Classification and regression trees. CRC Press, Boca Raton (1984)"},{"key":"10_CR7","doi-asserted-by":"publisher","DOI":"10.1016\/j.artint.2022.103822","volume":"314","author":"G Ciravegna","year":"2023","unstructured":"Ciravegna, G., Barbiero, P., Giannini, F., Gori, M., Li\u00f3, P., Maggini, M., Melacci, S.: Logic explained networks. Artif. Intell. 314, 103822 (2023)","journal-title":"Artif. Intell."},{"key":"10_CR8","doi-asserted-by":"publisher","DOI":"10.1017\/9781316219317","volume-title":"Picturing Quantum Processes - A first course in Quantum Theory and Diagrammatic Reasoning","author":"B Coecke","year":"2017","unstructured":"Coecke, B., Kissinger, A.: Picturing Quantum Processes - A first course in Quantum Theory and Diagrammatic Reasoning. Cambridge University Press, Cambridge (2017)"},{"key":"10_CR9","doi-asserted-by":"crossref","unstructured":"Costa, F., Ouyang, S., Dolog, P., Lawlor, A.: Automatic generation of natural language explanations. In: Proceedings of the 23rd International Conference on Intelligent User Interfaces Companion, pp.\u00a01\u20132 (2018)","DOI":"10.1145\/3180308.3180366"},{"key":"10_CR10","unstructured":"Cranmer, M.D., Xu, R., Battaglia, P., Ho, S.: Learning symbolic physics with graph networks. arXiv preprint arXiv:1909.05862 (2019)"},{"key":"10_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/978-3-030-99336-8_1","volume-title":"Programming Languages and Systems","author":"GSH Cruttwell","year":"2022","unstructured":"Cruttwell, G.S.H., Gavranovi\u0107, B., Ghani, N., Wilson, P., Zanasi, F.: Categorical foundations of gradient-based learning. In: ESOP 2022. LNCS, vol. 13240, pp. 1\u201328. Springer, Cham (2022). https:\/\/doi.org\/10.1007\/978-3-030-99336-8_1"},{"key":"10_CR12","unstructured":"Danilevsky, M., Qian, K., Aharonov, R., Katsis, Y., Kawas, B., Sen, P.: A survey of the state of explainable AI for natural language processing. arXiv preprint arXiv:2010.00711 (2020)"},{"key":"10_CR13","unstructured":"Das, A., Rad, P.: Opportunities and challenges in explainable artificial intelligence (xai): a survey. ArXiv arxiv:2006.11371 (2020)"},{"issue":"7887","key":"10_CR14","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1038\/s41586-021-04086-x","volume":"600","author":"A Davies","year":"2021","unstructured":"Davies, A., et al.: Advancing mathematics by guiding human intuition with AI. Nature 600(7887), 70\u201374 (2021)","journal-title":"Nature"},{"key":"10_CR15","doi-asserted-by":"crossref","unstructured":"Di\u00a0Lavore, E., de\u00a0Felice, G., Rom\u00e1n, M.: Monoidal streams for dataflow programming. In: Proceedings of the 37th Annual ACM\/IEEE Symposium on Logic in Computer Science. Association for Computing Machinery, New York (2022), https:\/\/doi.org\/10.1145\/3531130.3533365","DOI":"10.1145\/3531130.3533365"},{"key":"10_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1007\/978-3-030-90636-8_4","volume-title":"Formal Aspects of Component Software","author":"E Di Lavore","year":"2021","unstructured":"Di Lavore, E., Gianola, A., Rom\u00e1n, M., Sabadini, N., Soboci\u0144ski, P.: A canonical algebra of open transition systems. In: Sala\u00fcn, G., Wijs, A. (eds.) FACS 2021. LNCS, vol. 13077, pp. 63\u201381. Springer, Cham (2021). https:\/\/doi.org\/10.1007\/978-3-030-90636-8_4"},{"key":"10_CR17","doi-asserted-by":"crossref","unstructured":"Di\u00a0Martino, F., Delmastro, F.: Explainable AI for clinical and remote health applications: a survey on tabular and time series data. Artif. Intell. Rev. 1\u201355 (2022)","DOI":"10.1007\/s10462-022-10304-3"},{"key":"10_CR18","doi-asserted-by":"crossref","unstructured":"Doshi-Velez, F., Wallace, B.C., Adams, R.: Graph-sparse lda: a topic model with structured sparsity. In: Twenty-Ninth AAAI Conference on Artificial Intelligence (2015)","DOI":"10.1609\/aaai.v29i1.9603"},{"key":"10_CR19","doi-asserted-by":"crossref","unstructured":"Do\u0161ilovi\u0107, F.K., Br\u010di\u0107, M., Hlupi\u0107, N.: Explainable artificial intelligence: a survey. In: 2018 41st International Convention on Information and Communication Technology, Electronics and Microelectronics (MIPRO), pp. 0210\u20130215. IEEE (2018)","DOI":"10.23919\/MIPRO.2018.8400040"},{"issue":"5","key":"10_CR20","first-page":"329","volume":"47","author":"JM Dur\u00e1n","year":"2021","unstructured":"Dur\u00e1n, J.M., Jongsma, K.R.: Who is afraid of black box algorithms? on the epistemological and ethical basis of trust in medical AI. J. Med. Ethics 47(5), 329\u2013335 (2021)","journal-title":"J. Med. Ethics"},{"issue":"2","key":"10_CR21","doi-asserted-by":"publisher","first-page":"231","DOI":"10.2307\/1990284","volume":"58","author":"S Eilenberg","year":"1945","unstructured":"Eilenberg, S., MacLane, S.: General theory of natural equivalences. Trans. Am. Math. Soc. 58(2), 231\u2013294 (1945)","journal-title":"Trans. Am. Math. Soc."},{"issue":"1","key":"10_CR22","first-page":"1997","volume":"20","author":"T Elsken","year":"2019","unstructured":"Elsken, T., Metzen, J.H., Hutter, F.: Neural architecture search: a survey. J. Mach. Learn. Res. 20(1), 1997\u20132017 (2019)","journal-title":"J. Mach. Learn. Res."},{"key":"10_CR23","first-page":"21400","volume":"35","author":"M Espinosa Zarlenga","year":"2022","unstructured":"Espinosa Zarlenga, M., et al.: Concept embedding models: beyond the accuracy-explainability trade-off. Adv. Neural. Inf. Process. Syst. 35, 21400\u201321413 (2022)","journal-title":"Adv. Neural. Inf. Process. Syst."},{"key":"10_CR24","doi-asserted-by":"crossref","unstructured":"Fix, E., Hodges, J.L.: Discriminatory analysis. nonparametric discrimination: Consistency properties. Int. Stat. Rev.\/Revue Internationale de Statistique 57(3), 238\u2013247 (1989)","DOI":"10.2307\/1403797"},{"issue":"7","key":"10_CR25","doi-asserted-by":"publisher","first-page":"665","DOI":"10.1080\/00927877608822127","volume":"4","author":"T Fox","year":"1976","unstructured":"Fox, T.: Coalgebras and cartesian categories. Comm. Algebra 4(7), 665\u2013667 (1976)","journal-title":"Comm. Algebra"},{"key":"10_CR26","doi-asserted-by":"crossref","unstructured":"Friedman, J.H., Popescu, B.E.: Predictive learning via rule ensembles. Ann. Appl. Stat. 916\u2013954 (2008)","DOI":"10.1214\/07-AOAS148"},{"key":"10_CR27","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2020.107239","volume":"370","author":"T Fritz","year":"2020","unstructured":"Fritz, T.: A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statistics. Adv. Math. 370, 107239 (2020)","journal-title":"Adv. Math."},{"key":"10_CR28","unstructured":"Geiger, A., Potts, C., Icard, T.: Causal abstraction for faithful model interpretation. arXiv preprint arXiv:2301.04709 (2023)"},{"key":"10_CR29","doi-asserted-by":"crossref","unstructured":"Ghorbani, A., Abid, A., Zou, J.: Interpretation of neural networks is fragile. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol.\u00a033, pp. 3681\u20133688 (2019)","DOI":"10.1609\/aaai.v33i01.33013681"},{"key":"10_CR30","unstructured":"Ghorbani, A., Wexler, J., Zou, J., Kim, B.: Towards automatic concept-based explanations. arXiv preprint arXiv:1902.03129 (2019)"},{"key":"10_CR31","series-title":"Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence)","doi-asserted-by":"publisher","first-page":"52","DOI":"10.1007\/11524564_4","volume-title":"Conceptual Structures: Common Semantics for Sharing Knowledge","author":"J Goguen","year":"2005","unstructured":"Goguen, J.: What is a concept? In: Dau, F., Mugnier, M.-L., Stumme, G. (eds.) ICCS-ConceptStruct 2005. LNCS (LNAI), vol. 3596, pp. 52\u201377. Springer, Heidelberg (2005). https:\/\/doi.org\/10.1007\/11524564_4"},{"issue":"1","key":"10_CR32","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1145\/147508.147524","volume":"39","author":"JA Goguen","year":"1992","unstructured":"Goguen, J.A., Burstall, R.M.: Institutions: abstract model theory for specification and programming. J. ACM (JACM) 39(1), 95\u2013146 (1992)","journal-title":"J. ACM (JACM)"},{"key":"10_CR33","unstructured":"Guidotti, R., Monreale, A., Ruggieri, S., Pedreschi, D., Turini, F., Giannotti, F.: Local rule-based explanations of black box decision systems. arXiv preprint arXiv:1805.10820 (2018)"},{"issue":"37","key":"10_CR34","doi-asserted-by":"publisher","first-page":"eaay7120","DOI":"10.1126\/scirobotics.aay7120","volume":"4","author":"D Gunning","year":"2019","unstructured":"Gunning, D., Stefik, M., Choi, J., Miller, T., Stumpf, S., Yang, G.Z.: Xai-explainable artificial intelligence. Sci. Rob. 4(37), eaay7120 (2019)","journal-title":"Sci. Rob."},{"key":"10_CR35","doi-asserted-by":"crossref","unstructured":"Hastie, T.J.: Generalized additive models. In: Statistical Models in S, pp. 249\u2013307. Routledge (2017)","DOI":"10.1201\/9780203738535-7"},{"issue":"8","key":"10_CR36","doi-asserted-by":"publisher","first-page":"1735","DOI":"10.1162\/neco.1997.9.8.1735","volume":"9","author":"S Hochreiter","year":"1997","unstructured":"Hochreiter, S., Schmidhuber, J.: Long short-term memory. Neural Comput. 9(8), 1735\u20131780 (1997)","journal-title":"Neural Comput."},{"key":"10_CR37","unstructured":"Hoffman, R.R., Mueller, S.T., Klein, G., Litman, J.: Metrics for explainable ai: challenges and prospects. arXiv preprint arXiv:1812.04608 (2018)"},{"issue":"8","key":"10_CR38","doi-asserted-by":"publisher","first-page":"2554","DOI":"10.1073\/pnas.79.8.2554","volume":"79","author":"JJ Hopfield","year":"1982","unstructured":"Hopfield, J.J.: Neural networks and physical systems with emergent collective computational abilities. Proc. Natl. Acad. Sci. 79(8), 2554\u20132558 (1982)","journal-title":"Proc. Natl. Acad. Sci."},{"issue":"10","key":"10_CR39","doi-asserted-by":"publisher","first-page":"573","DOI":"10.1038\/s42256-020-00236-4","volume":"2","author":"J Jim\u00e9nez-Luna","year":"2020","unstructured":"Jim\u00e9nez-Luna, J., Grisoni, F., Schneider, G.: Drug discovery with explainable artificial intelligence. Nat. Mach. Intell. 2(10), 573\u2013584 (2020)","journal-title":"Nat. Mach. Intell."},{"issue":"1","key":"10_CR40","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1016\/0001-8708(91)90003-P","volume":"88","author":"A Joyal","year":"1991","unstructured":"Joyal, A., Street, R.: The geometry of tensor calculus, i. Adv. Math. 88(1), 55\u2013112 (1991)","journal-title":"Adv. Math."},{"key":"10_CR41","unstructured":"Kahneman, D.: Thinking, Fast and Slow. Macmillan, New York (2011)"},{"key":"10_CR42","doi-asserted-by":"crossref","unstructured":"Karasmanoglou, A., Antonakakis, M., Zervakis, M.: Heatmap-based explanation of yolov5 object detection with layer-wise relevance propagation. In: 2022 IEEE International Conference on Imaging Systems and Techniques (IST), pp.\u00a01\u20136. IEEE (2022)","DOI":"10.1109\/IST55454.2022.9827744"},{"issue":"2","key":"10_CR43","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1051\/ita:2002009","volume":"36","author":"P Katis","year":"2002","unstructured":"Katis, P., Sabadini, N., Walters, R.F.C.: Feedback, trace and fixed-point semantics. RAIRO-Theor. Inf. Appl. 36(2), 181\u2013194 (2002)","journal-title":"RAIRO-Theor. Inf. Appl."},{"key":"10_CR44","unstructured":"Kaufmann, L.: Clustering by means of medoids. In: Proceedings of Statistical Data Analysis Based on the L1 Norm Conference, Neuchatel, 1987, pp. 405\u2013416 (1987)"},{"key":"10_CR45","unstructured":"Kim, B., Khanna, R., Koyejo, O.O.: Examples are not enough, learn to criticize! criticism for interpretability. Adv. Neural Inf. Process. Syst. 29 (2016)"},{"key":"10_CR46","unstructured":"Kingma, D.P., Ba, J.: Adam: a method for stochastic optimization. arXiv preprint arXiv:1412.6980 (2014)"},{"key":"10_CR47","unstructured":"Koh, P.W., et al.: Concept bottleneck models. In: International Conference on Machine Learning, pp. 5338\u20135348. PMLR (2020)"},{"key":"10_CR48","doi-asserted-by":"publisher","unstructured":"Kulkarni, A., Shivananda, A., Sharma, N.R.: Explainable AI for computer vision. In: Computer Vision Projects with PyTorch, pp. 325\u2013340. Springer, Heidelberg (2022). https:\/\/doi.org\/10.1007\/978-1-4842-8273-1_10","DOI":"10.1007\/978-1-4842-8273-1_10"},{"issue":"3","key":"10_CR49","doi-asserted-by":"publisher","first-page":"1350","DOI":"10.1214\/15-AOAS848","volume":"9","author":"B Letham","year":"2015","unstructured":"Letham, B., Rudin, C., McCormick, T.H., Madigan, D., et al.: Interpretable classifiers using rules and bayesian analysis: building a better stroke prediction model. Ann. Appl. Stat. 9(3), 1350\u20131371 (2015)","journal-title":"Ann. Appl. Stat."},{"key":"10_CR50","unstructured":"Li, Y., Zhou, J., Verma, S., Chen, F.: A survey of explainable graph neural networks: Taxonomy and evaluation metrics. arXiv preprint arXiv:2207.12599 (2022)"},{"issue":"1","key":"10_CR51","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1057\/s41599-020-0492-6","volume":"7","author":"S Lo Piano","year":"2020","unstructured":"Lo Piano, S.: Ethical principles in machine learning and artificial intelligence: cases from the field and possible ways forward. Human. Social Sci. Commun. 7(1), 1\u20137 (2020)","journal-title":"Human. Social Sci. Commun."},{"key":"10_CR52","unstructured":"Lundberg, S., Lee, S.I.: A unified approach to interpreting model predictions. arXiv preprint arXiv:1705.07874 (2017)"},{"key":"10_CR53","doi-asserted-by":"publisher","unstructured":"Mac Lane, S.: Categories for the Working Mathematician. Graduate Texts in Mathematics. Springer, New York (1978). https:\/\/doi.org\/10.1007\/978-1-4757-4721-8","DOI":"10.1007\/978-1-4757-4721-8"},{"key":"10_CR54","unstructured":"Manhaeve, R., Dumancic, S., Kimmig, A., Demeester, T., De\u00a0Raedt, L.: Deepproblog: neural probabilistic logic programming. Adv. Neural Inf. Process. Syst. 31 (2018)"},{"key":"10_CR55","unstructured":"Marcus, G.: The next decade in AI: four steps towards robust artificial intelligence. arXiv preprint arXiv:2002.06177 (2020)"},{"key":"10_CR56","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":"5","key":"10_CR57","doi-asserted-by":"publisher","first-page":"3503","DOI":"10.1007\/s10462-021-10088-y","volume":"55","author":"D Minh","year":"2022","unstructured":"Minh, D., Wang, H.X., Li, Y.F., Nguyen, T.N.: Explainable artificial intelligence: a comprehensive review. Artif. Intell. Rev. 55(5), 3503\u20133568 (2022)","journal-title":"Artif. Intell. Rev."},{"key":"10_CR58","unstructured":"Molnar, C.: Interpretable machine learning (2020).https:\/\/www.lulu.com\/"},{"issue":"3","key":"10_CR59","doi-asserted-by":"publisher","first-page":"370","DOI":"10.2307\/2344614","volume":"135","author":"JA Nelder","year":"1972","unstructured":"Nelder, J.A., Wedderburn, R.W.: Generalized linear models. J. Roy. Stat. Soc.: Ser. A (Gen.) 135(3), 370\u2013384 (1972)","journal-title":"J. Roy. Stat. Soc.: Ser. A (Gen.)"},{"key":"10_CR60","unstructured":"Ong, E., Veli\u010dkovi\u0107, P.: Learnable commutative monoids for graph neural networks. arXiv preprint arXiv:2212.08541 (2022)"},{"key":"10_CR61","doi-asserted-by":"crossref","unstructured":"Palacio, S., Lucieri, A., Munir, M., Ahmed, S., Hees, J., Dengel, A.: Xai handbook: towards a unified framework for explainable AI. In: Proceedings of the IEEE\/CVF International Conference on Computer Vision, pp. 3766\u20133775 (2021)","DOI":"10.1109\/ICCVW54120.2021.00420"},{"key":"10_CR62","unstructured":"Petsiuk, V., Das, A., Saenko, K.: Rise: randomized input sampling for explanation of black-box models. arXiv preprint arXiv:1806.07421 (2018)"},{"key":"10_CR63","unstructured":"Prawitz, D.: Natural Deduction: A Proof-Theoretical Study. Courier Dover Publications, Mineola (2006)"},{"key":"10_CR64","doi-asserted-by":"crossref","unstructured":"Ribeiro, M.T., Singh, S., Guestrin, C.: \u201cwhy should i trust you?\" explaining the predictions of any classifier. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 1135\u20131144 (2016)","DOI":"10.1145\/2939672.2939778"},{"key":"10_CR65","unstructured":"Ribeiro, M.T., Singh, S., Guestrin, C.: Model-agnostic interpretability of machine learning. arXiv preprint arXiv:1606.05386 (2016)"},{"key":"10_CR66","doi-asserted-by":"crossref","unstructured":"Ribeiro, M.T., Singh, S., Guestrin, C.: Anchors: high-precision model-agnostic explanations. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol.\u00a032 (2018)","DOI":"10.1609\/aaai.v32i1.11491"},{"key":"10_CR67","unstructured":"Riley, M.: Categories of optics. arXiv preprint arXiv:1809.00738 (2018)"},{"issue":"5","key":"10_CR68","doi-asserted-by":"publisher","first-page":"206","DOI":"10.1038\/s42256-019-0048-x","volume":"1","author":"C Rudin","year":"2019","unstructured":"Rudin, C.: Stop explaining black box machine learning models for high stakes decisions and use interpretable models instead. Nat. Mach. Intell. 1(5), 206\u2013215 (2019)","journal-title":"Nat. Mach. Intell."},{"key":"10_CR69","doi-asserted-by":"crossref","unstructured":"Rumelhart, D.E., Hinton, G.E., Williams, R.J.: Learning internal representations by error propagation. Technical report, California Univ San Diego La Jolla Inst for Cognitive Science (1985)","DOI":"10.21236\/ADA164453"},{"issue":"4","key":"10_CR70","doi-asserted-by":"publisher","first-page":"1307","DOI":"10.1137\/0907087","volume":"7","author":"F Santosa","year":"1986","unstructured":"Santosa, F., Symes, W.W.: Linear inversion of band-limited reflection seismograms. SIAM J. Sci. Stat. Comput. 7(4), 1307\u20131330 (1986)","journal-title":"SIAM J. Sci. Stat. Comput."},{"issue":"5923","key":"10_CR71","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1126\/science.1165893","volume":"324","author":"M Schmidt","year":"2009","unstructured":"Schmidt, M., Lipson, H.: Distilling free-form natural laws from experimental data. Science 324(5923), 81\u201385 (2009)","journal-title":"Science"},{"key":"10_CR72","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1017\/S096012950000311X","volume":"11","author":"P Selinger","year":"2001","unstructured":"Selinger, P.: Control categories and duality: on the categorical semantics of the lambda-mu calculus. Math. Struct. Comput. Sci. 11, 207\u2013260 (2001)","journal-title":"Math. Struct. Comput. Sci."},{"key":"10_CR73","doi-asserted-by":"crossref","unstructured":"Selvaraju, R.R., Cogswell, M., Das, A., Vedantam, R., Parikh, D., Batra, D.: Grad-cam: Visual explanations from deep networks via gradient-based localization. In: Proceedings of the IEEE International Conference on Computer Vision, pp. 618\u2013626 (2017)","DOI":"10.1109\/ICCV.2017.74"},{"key":"10_CR74","unstructured":"Shiebler, D., Gavranovi\u0107, B., Wilson, P.: Category theory in machine learning. arXiv preprint arXiv:2106.07032 (2021)"},{"key":"10_CR75","unstructured":"Simonyan, K., Vedaldi, A., Zisserman, A.: Deep inside convolutional networks: visualising image classification models and saliency maps. arXiv preprint arXiv:1312.6034 (2013)"},{"key":"10_CR76","doi-asserted-by":"publisher","unstructured":"Sprunger, D., Katsumata, S.: Differentiable causal computations via delayed trace. In: 34th Annual ACM\/IEEE Symposium on Logic in Computer Science, LICS 2019, Vancouver, BC, Canada, 24\u201327 June 2019, pp. 1\u201312. IEEE (2019). https:\/\/doi.org\/10.1109\/LICS.2019.8785670","DOI":"10.1109\/LICS.2019.8785670"},{"key":"10_CR77","doi-asserted-by":"publisher","unstructured":"Stein, D., Staton, S.: Compositional semantics for probabilistic programs with exact conditioning. In: 2021 36th Annual ACM\/IEEE Symposium on Logic in Computer Science (LICS), pp. 1\u201313 (2021).https:\/\/doi.org\/10.1109\/LICS52264.2021.9470552","DOI":"10.1109\/LICS52264.2021.9470552"},{"key":"10_CR78","doi-asserted-by":"publisher","unstructured":"Swan, J., Nivel, E., Kant, N., Hedges, J., Atkinson, T., Steunebrink, B.: A compositional framework. In: The Road to General Intelligence, pp. 73\u201390. Springer, Cham (2022). https:\/\/doi.org\/10.1007\/978-3-031-08020-3_9","DOI":"10.1007\/978-3-031-08020-3_9"},{"key":"10_CR79","unstructured":"Takeuti, G.: Proof Theory, vol.\u00a081. Courier Corporation, Mineola (2013)"},{"issue":"3","key":"10_CR80","doi-asserted-by":"publisher","first-page":"341","DOI":"10.2307\/2102968","volume":"4","author":"A Tarski","year":"1944","unstructured":"Tarski, A.: The semantic conception of truth: and the foundations of semantics. Phil. Phenomenol. Res. 4(3), 341\u2013376 (1944)","journal-title":"Phil. Phenomenol. Res."},{"issue":"1","key":"10_CR81","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1111\/j.2517-6161.1996.tb02080.x","volume":"58","author":"R Tibshirani","year":"1996","unstructured":"Tibshirani, R.: Regression shrinkage and selection via the lasso. J. Roy. Stat. Soc.: Ser. B (Methodol.) 58(1), 267\u2013288 (1996)","journal-title":"J. Roy. Stat. Soc.: Ser. B (Methodol.)"},{"issue":"11","key":"10_CR82","doi-asserted-by":"publisher","first-page":"4793","DOI":"10.1109\/TNNLS.2020.3027314","volume":"32","author":"E Tjoa","year":"2020","unstructured":"Tjoa, E., Guan, C.: A survey on explainable artificial intelligence (xai): toward medical xai. IEEE Trans. Neural Netw. Learn. Syst. 32(11), 4793\u20134813 (2020)","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"10_CR83","doi-asserted-by":"crossref","unstructured":"Turi, D., Plotkin, G.D.: Towards a mathematical operational semantics. In: Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science, pp. 280\u2013291 (1997)","DOI":"10.1109\/LICS.1997.614955"},{"key":"10_CR84","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"2","DOI":"10.1007\/11575467_2","volume-title":"Programming Languages and Systems","author":"T Uustalu","year":"2005","unstructured":"Uustalu, T., Vene, V.: The essence of dataflow programming. In: Yi, K. (ed.) APLAS 2005. LNCS, vol. 3780, pp. 2\u201318. Springer, Heidelberg (2005). https:\/\/doi.org\/10.1007\/11575467_2"},{"issue":"5","key":"10_CR85","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1016\/j.entcs.2008.05.029","volume":"203","author":"T Uustalu","year":"2008","unstructured":"Uustalu, T., Vene, V.: Comonadic notions of computation. Electron. Notes Theor. Comput. Sci. 203(5), 263\u2013284 (2008)","journal-title":"Electron. Notes Theor. Comput. Sci."},{"key":"10_CR86","unstructured":"Vaswani, A., et al.: Attention is all you need. Adv. Neural Inf. Process. Syst. 30 (2017)"},{"key":"10_CR87","first-page":"1","volume":"18","author":"PF Verhulst","year":"1845","unstructured":"Verhulst, P.F.: Resherches mathematiques sur la loi d\u2019accroissement de la population. Nouveaux memoires de l\u2019academie royale des sciences 18, 1\u201341 (1845)","journal-title":"Nouveaux memoires de l\u2019academie royale des sciences"},{"key":"10_CR88","first-page":"841","volume":"31","author":"S Wachter","year":"2017","unstructured":"Wachter, S., Mittelstadt, B., Russell, C.: Counterfactual explanations without opening the black box: automated decisions and the GDPR. Harv. JL Tech. 31, 841 (2017)","journal-title":"Harv. JL Tech."},{"key":"10_CR89","doi-asserted-by":"publisher","first-page":"399","DOI":"10.1016\/j.ress.2015.05.018","volume":"142","author":"P Wei","year":"2015","unstructured":"Wei, P., Lu, Z., Song, J.: Variable importance analysis: a comprehensive review. Reliabil. Eng. Syst. Saf. 142, 399\u2013432 (2015)","journal-title":"Reliabil. Eng. Syst. Saf."},{"key":"10_CR90","doi-asserted-by":"publisher","first-page":"247","DOI":"10.4204\/EPTCS.333.17","volume":"333","author":"P Wilson","year":"2021","unstructured":"Wilson, P., Zanasi, F.: Reverse derivative ascent: a categorical approach to learning Boolean circuits. Electron. Proc. Theor. Comput. Sci. 333, 247\u2013260 (2021)","journal-title":"Electron. Proc. Theor. Comput. Sci."},{"key":"10_CR91","doi-asserted-by":"crossref","unstructured":"Yang, H., Rudin, C., Seltzer, M.: Scalable bayesian rule lists. In: International Conference on Machine Learning, pp. 3921\u20133930. PMLR (2017)","DOI":"10.32614\/CRAN.package.sbrl"},{"key":"10_CR92","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"818","DOI":"10.1007\/978-3-319-10590-1_53","volume-title":"Computer Vision \u2013 ECCV 2014","author":"MD Zeiler","year":"2014","unstructured":"Zeiler, M.D., Fergus, R.: Visualizing and understanding convolutional networks. In: Fleet, D., Pajdla, T., Schiele, B., Tuytelaars, T. (eds.) ECCV 2014. LNCS, vol. 8689, pp. 818\u2013833. Springer, Cham (2014). https:\/\/doi.org\/10.1007\/978-3-319-10590-1_53"},{"key":"10_CR93","unstructured":"Zintgraf, L.M., Cohen, T.S., Adel, T., Welling, M.: Visualizing deep neural network decisions: prediction difference analysis. arXiv preprint arXiv:1702.04595 (2017)"}],"container-title":["Communications in Computer and Information Science","Explainable Artificial Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-63800-8_10","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,11,23]],"date-time":"2024-11-23T19:19:46Z","timestamp":1732389586000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-63800-8_10"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024]]},"ISBN":["9783031637995","9783031638008"],"references-count":93,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-63800-8_10","relation":{},"ISSN":["1865-0929","1865-0937"],"issn-type":[{"type":"print","value":"1865-0929"},{"type":"electronic","value":"1865-0937"}],"subject":[],"published":{"date-parts":[[2024]]},"assertion":[{"value":"10 July 2024","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"The authors have no competing interests.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Disclosure of Interests"}},{"value":"xAI","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"World Conference on Explainable Artificial Intelligence","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Valletta","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Malta","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2024","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"17 July 2024","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"19 July 2024","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"xai2024","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/xaiworldconference.com\/2024\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}