{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,10]],"date-time":"2026-06-10T16:40:23Z","timestamp":1781109623741,"version":"3.54.1"},"reference-count":54,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T00:00:00Z","timestamp":1760313600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T00:00:00Z","timestamp":1760313600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"CISPA - Helmholtz-Zentrum f\u00fcr Informationssicherheit gGmbH"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Acta Informatica"],"published-print":{"date-parts":[[2025,12]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    Explainability is emerging as a key requirement for autonomous systems. While many works have focused on what constitutes a valid explanation, few have considered formalizing explainability as a system property. In this work, we approach this problem from the perspective of hyperproperties. We start with a combination of three prominent flavors of modal logic and show how they can be used for specifying and verifying counterfactual explainability in multi-agent systems: With Lewis\u2019 counterfactuals, linear-time temporal logic, and a knowledge modality, we can reason about whether agents know\n                    <jats:italic>why<\/jats:italic>\n                    a specific observation occurs, i.e., whether that observation is\n                    <jats:italic>explainable<\/jats:italic>\n                    to them. We use this logic to formalize multiple notions of explainability on the system level. We then show how this logic can be embedded into a hyperlogic. Notably, from this analysis we conclude that the model-checking problem of our logic is decidable, which paves the way for the automated verification of explainability requirements.\n                  <\/jats:p>","DOI":"10.1007\/s00236-025-00507-w","type":"journal-article","created":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T06:38:35Z","timestamp":1760337515000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Explainability requirements as hyperproperties"],"prefix":"10.1007","volume":"62","author":[{"given":"Bernd","family":"Finkbeiner","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Julian","family":"Siber","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,10,13]]},"reference":[{"key":"507_CR1","doi-asserted-by":"publisher","unstructured":"Aguilera-Ventura, C., Herzig, A., Liu, X., et\u00a0al.: Counterfactual reasoning via grounded distance. In: Marquis P, Son TC, Kern-Isberner G (eds) Proceedings of the 20th International Conference on Principles of Knowledge Representation and Reasoning, KR 2023, Rhodes, Greece, September 2-8, 2023, pp 2\u201311, https:\/\/doi.org\/10.24963\/kr.2023\/1 (2023)","DOI":"10.24963\/kr.2023\/1"},{"key":"507_CR2","doi-asserted-by":"publisher","unstructured":"Almagor, S., Lahijanian, M.: Explainable multi agent path finding. In: Seghrouchni AEF, Sukthankar G, An B, et\u00a0al (eds) Proceedings of the 19th International Conference on Autonomous Agents and Multiagent Systems, AAMAS \u201920, Auckland, New Zealand, May 9-13, 2020. International Foundation for Autonomous Agents and Multiagent Systems, https:\/\/doi.org\/10.5555\/3398761.3398771 (2020)","DOI":"10.5555\/3398761.3398771"},{"key":"507_CR3","doi-asserted-by":"publisher","unstructured":"Audemard, G., Koriche, F., Marquis, P.: On tractable XAI queries based on compiled representations. In: Calvanese D, Erdem E, Thielscher M (eds) Proceedings of the 17th International Conference on Principles of Knowledge Representation and Reasoning, KR 2020, Rhodes, Greece, September 12-18, 2020, pp 838\u2013849, https:\/\/doi.org\/10.24963\/kr.2020\/86 (2020)","DOI":"10.24963\/kr.2020\/86"},{"key":"507_CR4","doi-asserted-by":"publisher","unstructured":"Balliu, M., Dam, M., Guernic, G.L.: Epistemic temporal logic for information flow security. In: Askarov A, Guttman JD (eds) Proceedings of the 2011 Workshop on Programming Languages and Analysis for Security, PLAS 2011, San Jose, CA, USA, 5 June, 2011. ACM, p\u00a06, (2011). https:\/\/doi.org\/10.1145\/2166956.2166962","DOI":"10.1145\/2166956.2166962"},{"key":"507_CR5","unstructured":"Beckers, S.: Causal explanations and XAI. In: Sch\u00f6lkopf B, Uhler C, Zhang K (eds) 1st Conference on Causal Learning and Reasoning, CLeaR 2022, Sequoia Conference Center, Eureka, CA, USA, 11-13 April, 2022, Proceedings of Machine Learning Research, vol 177. PMLR, pp 90\u2013109, (2022). https:\/\/proceedings.mlr.press\/v177\/beckers22a.html"},{"key":"507_CR6","unstructured":"Bozzelli, L., Maubert, B., Pinchinat, S.: Unifying hyper and epistemic temporal logic. CoRR abs\/1409.2711, (2014). http:\/\/arxiv.org\/abs\/1409.2711"},{"key":"507_CR7","doi-asserted-by":"publisher","unstructured":"Bozzelli, L., Maubert, B., Pinchinat, S.: Unifying hyper and epistemic temporal logics. In: Pitts AM (ed) Foundations of Software Science and Computation Structures - 18th International Conference, FoSSaCS 2015, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2015, London, UK, April 11-18, 2015. Proceedings, Lecture Notes in Computer Science, vol 9034. Springer, pp 167\u2013182, (2015). https:\/\/doi.org\/10.1007\/978-3-662-46678-0_11","DOI":"10.1007\/978-3-662-46678-0_11"},{"issue":"1","key":"507_CR8","doi-asserted-by":"publisher","first-page":"8:1","DOI":"10.1145\/3637212","volume":"25","author":"L Bozzelli","year":"2024","unstructured":"Bozzelli, L., Maubert, B., Murano, A.: On the complexity of model checking knowledge and time. ACM Trans Comput Log 25(1), 8:1-8:42 (2024). https:\/\/doi.org\/10.1145\/3637212","journal-title":"ACM Trans Comput Log"},{"key":"507_CR9","doi-asserted-by":"publisher","unstructured":"Brandao, M., Mansouri, M., Mohammed, A., et\u00a0al.: Explainability in multi-agent path\/motion planning: User-study-driven taxonomy and requirements. In: Faliszewski P, Mascardi V, Pelachaud C, et\u00a0al (eds) 21st International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2022, Auckland, New Zealand, May 9-13, 2022. International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS), pp 172\u2013180, (2022). https:\/\/doi.org\/10.5555\/3535850.3535871, https:\/\/www.ifaamas.org\/Proceedings\/aamas2022\/pdfs\/p172.pdf","DOI":"10.5555\/3535850.3535871"},{"key":"507_CR10","doi-asserted-by":"crossref","unstructured":"Carelli, M., Finkbeiner, B., Siber, J.: Closure and complexity of temporal causality. In: 40th Annual ACM\/IEEE Symposium on Logic in Computer Science, LICS 2025, Singapore, June 23-26, 2025. IEEE (2025)","DOI":"10.1109\/LICS65433.2025.00015"},{"key":"507_CR11","volume-title":"The Stanford Encyclopedia of Philosophy, Fall","author":"W Carnielli","year":"2020","unstructured":"Carnielli, W., Coniglio, M.E.: Combining logics. In: Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy, Fall, 2020th edn. Stanford University, Metaphysics Research Lab (2020)","edition":"2020"},{"issue":"6","key":"507_CR12","doi-asserted-by":"publisher","first-page":"1157","DOI":"10.3233\/JCS-2009-0393","volume":"18","author":"MR Clarkson","year":"2010","unstructured":"Clarkson, M.R., Schneider, F.B.: Hyperproperties. J Comput Secur 18(6), 1157\u20131210 (2010). https:\/\/doi.org\/10.3233\/JCS-2009-0393","journal-title":"Hyperproperties. J Comput Secur"},{"key":"507_CR13","doi-asserted-by":"publisher","unstructured":"Coenen, N., Finkbeiner, B., Hahn, C., et\u00a0al.: The hierarchy of hyperlogics. In: 34th Annual ACM\/IEEE Symposium on Logic in Computer Science, LICS 2019, Vancouver, BC, Canada, June 24-27, 2019. IEEE, pp 1\u201313, (2019). https:\/\/doi.org\/10.1109\/LICS.2019.8785713","DOI":"10.1109\/LICS.2019.8785713"},{"key":"507_CR14","doi-asserted-by":"publisher","unstructured":"Coenen, N., Dachselt, R., Finkbeiner, B., et\u00a0al.: Explaining hyperproperty violations. In: Shoham S, Vizel Y (eds) Computer Aided Verification - 34th International Conference, CAV 2022, Haifa, Israel, August 7-10, 2022, Proceedings, Part I, Lecture Notes in Computer Science, vol 13371. Springer, pp 407\u2013429, , (2022a). https:\/\/doi.org\/10.1007\/978-3-031-13185-1_20","DOI":"10.1007\/978-3-031-13185-1_20"},{"key":"507_CR15","doi-asserted-by":"publisher","unstructured":"Coenen, N., Finkbeiner, B., Frenkel, H., et\u00a0al.: Temporal causality in reactive systems. In: Bouajjani A, Hol\u00edk L, Wu Z (eds) Automated Technology for Verification and Analysis - 20th International Symposium, ATVA 2022, Virtual Event, October 25-28, 2022, Proceedings, Lecture Notes in Computer Science, vol 13505. Springer, pp 208\u2013224, (2022b). https:\/\/doi.org\/10.1007\/978-3-031-19992-9_13","DOI":"10.1007\/978-3-031-19992-9_13"},{"key":"507_CR16","doi-asserted-by":"crossref","unstructured":"Darwiche, A., Ji, C.: x On the computation of necessary and sufficient explanations. In: Thirty-Sixth AAAI Conference on Artificial Intelligence, AAAI 2022, Thirty-Fourth Conference on Innovative Applications of Artificial Intelligence, IAAI 2022, The Twelveth Symposium on Educational Advances in Artificial Intelligence, EAAI 2022 Virtual Event, February 22 - March 1, 2022. AAAI Press, pp 5582\u20135591, (2022). https:\/\/ojs.aaai.org\/index.php\/AAAI\/article\/view\/20498","DOI":"10.1609\/aaai.v36i5.20498"},{"key":"507_CR17","doi-asserted-by":"publisher","DOI":"10.7551\/mitpress\/5803.001.0001","author":"R Fagin","year":"1995","unstructured":"Fagin, R., Halpern, J.Y., Moses, Y., et al.: Reasoning about knowledge. MIT Press (1995). https:\/\/doi.org\/10.7551\/mitpress\/5803.001.0001","journal-title":"MIT Press"},{"key":"507_CR18","doi-asserted-by":"publisher","unstructured":"Finkbeiner, B., Siber, J.: Counterfactuals modulo temporal logics. In: Piskac R, Voronkov A (eds) LPAR 2023: Proceedings of 24th International Conference on Logic for Programming, Artificial Intelligence and Reasoning, Manizales, Colombia, 4-9th June 2023, EPiC Series in Computing, vol\u00a094. EasyChair, pp 181\u2013204, https:\/\/doi.org\/10.29007\/qtw7, (2023)","DOI":"10.29007\/qtw7"},{"key":"507_CR19","doi-asserted-by":"publisher","unstructured":"Finkbeiner, B., Zimmermann, M.: The first-order logic of hyperproperties. In: Vollmer H, Vall\u00e9e B (eds) 34th Symposium on Theoretical Aspects of Computer Science, STACS 2017, March 8-11, 2017, Hannover, Germany, LIPIcs, vol\u00a066. Schloss Dagstuhl - Leibniz-Zentrum f\u00fcr Informatik, pp 30:1\u201330:14, (2017). https:\/\/doi.org\/10.4230\/LIPIcs.STACS.2017.30","DOI":"10.4230\/LIPIcs.STACS.2017.30"},{"key":"507_CR20","doi-asserted-by":"publisher","unstructured":"Finkbeiner, B., Frenkel, H., Metzger, N., et\u00a0al.: Synthesis of temporal causality. In: Gurfinkel A, Ganesh V (eds) Computer Aided Verification - 36th International Conference, CAV 2024, Montreal, QC, Canada, July 24-27, 2024, Proceedings, Part III, Lecture Notes in Computer Science, vol 14683. Springer, pp 87\u2013111, (2024). https:\/\/doi.org\/10.1007\/978-3-031-65633-0_5","DOI":"10.1007\/978-3-031-65633-0_5"},{"key":"507_CR21","unstructured":"Finkbeiner, B., Frenkel, H., Siber, J.: An information-flow perspective on explainability requirements: Specification and verification. In: 22nd International Conference on Principles of Knowledge Representation and Reasoning, KR 2025, Melbourne, Australia, November 11-17, 2025, (to appear) (2025)"},{"key":"507_CR22","unstructured":"Goyal, Y., Wu, Z., Ernst, J., et\u00a0al.: Counterfactual visual explanations. In: Chaudhuri K, Salakhutdinov R (eds) Proceedings of the 36th International Conference on Machine Learning, ICML 2019, 9-15 June 2019, Long Beach, California, USA, Proceedings of Machine Learning Research, vol\u00a097. PMLR, pp 2376\u20132384, (2019). http:\/\/proceedings.mlr.press\/v97\/goyal19a.html"},{"issue":"3","key":"507_CR23","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1007\/s001820050113","volume":"28","author":"JY Halpern","year":"1999","unstructured":"Halpern, J.Y.: Hypothetical knowledge and counterfactual reasoning. Int. J. Game Theory 28(3), 315\u2013330 (1999). https:\/\/doi.org\/10.1007\/s001820050113","journal-title":"Int. J. Game Theory"},{"key":"507_CR24","doi-asserted-by":"publisher","unstructured":"Halpern, J.Y., O\u2019Neill, K.R.: Secrecy in multiagent systems. ACM Trans Inf Syst Secur 12(1), 5:1\u20135:47 (2008). https:\/\/doi.org\/10.1145\/1410234.1410239","DOI":"10.1145\/1410234.1410239"},{"key":"507_CR25","doi-asserted-by":"crossref","unstructured":"Halpern JY, Pearl J (2005a) Causes and explanations: A structural-model approach. part i:Causes. The British Journal for the Philosophy of Science 56(4):843\u2013887. http:\/\/www.jstor.org\/stable\/3541870","DOI":"10.1093\/bjps\/axi147"},{"issue":"4","key":"507_CR26","doi-asserted-by":"publisher","first-page":"889","DOI":"10.1093\/bjps\/axi148","volume":"56","author":"JY Halpern","year":"2005","unstructured":"Halpern, J.Y., Pearl, J.: Causes and explanations A structural-model approach. Explanations part ii: The British Journal for the Philosophy of Science 56(4), 889\u2013911 (2005). (http:\/\/www.jstor.org\/stable\/3541871)","journal-title":"The British Journal for the Philosophy of Science"},{"issue":"3","key":"507_CR27","doi-asserted-by":"publisher","first-page":"674","DOI":"10.1137\/S0097539797320906","volume":"33","author":"JY Halpern","year":"2004","unstructured":"Halpern, J.Y., van der Meyden, R., Vardi, M.Y.: Complete axiomatizations for reasoning about knowledge and time. SIAM J. Comput. 33(3), 674\u2013703 (2004). https:\/\/doi.org\/10.1137\/S0097539797320906","journal-title":"SIAM J. Comput."},{"key":"507_CR28","unstructured":"Hofmann J.: Logical methods for the hierarchy of hyperlogics. PhD thesis, Saarland University, Saarbr\u00fccken, Germany, (2022). https:\/\/publikationen.sulb.uni-saarland.de\/handle\/20.500.11880\/35154"},{"key":"507_CR29","doi-asserted-by":"publisher","unstructured":"Horak, T., Coenen, N., Metzger, N., et al.: Visual analysis of hyperproperties for understanding model checking results. IEEE Trans Vis Comput Graph 28(1), 357\u2013367 (2022). https:\/\/doi.org\/10.1109\/TVCG.2021.3114866","DOI":"10.1109\/TVCG.2021.3114866"},{"key":"507_CR30","unstructured":"Kamp, J.A.W.: Tense logic and the theory of linear order. University of California, Los Angeles (1968)"},{"key":"507_CR31","doi-asserted-by":"publisher","unstructured":"Khan, S.M., Lesp\u00e9rance, Y.: Knowing why - on the dynamics of knowledge about actual causes in the situation calculus. In: Dignum F, Lomuscio A, Endriss U, et\u00a0al (eds) AAMAS \u201921: 20th International Conference on Autonomous Agents and Multiagent Systems, Virtual Event, United Kingdom, May 3-7, 2021. ACM, pp 701\u2013709, (2021). https:\/\/doi.org\/10.5555\/3463952.3464037, https:\/\/www.ifaamas.org\/Proceedings\/aamas2021\/pdfs\/p701.pdf","DOI":"10.5555\/3463952.3464037"},{"key":"507_CR32","doi-asserted-by":"publisher","unstructured":"Khan, S.M., Rostamigiv, M.: On explaining agent behaviour via root cause analysis: A formal account grounded in theory of mind. In: Gal K, Now\u00e9 A, Nalepa GJ, et\u00a0al (eds) ECAI 2023 - 26th European Conference on Artificial Intelligence, September 30 - October 4, 2023, Krak\u00f3w, Poland - Including 12th Conference on Prestigious Applications of Intelligent Systems (PAIS 2023), Frontiers in Artificial Intelligence and Applications, vol 372. IOS Press, pp 1239\u20131247, (2023). https:\/\/doi.org\/10.3233\/FAIA230401","DOI":"10.3233\/FAIA230401"},{"key":"507_CR33","doi-asserted-by":"publisher","unstructured":"K\u00f6hl, M.A., Baum, K., Langer, M., et\u00a0al.: Explainability as a non-functional requirement. In: Damian DE, Perini A, Lee S (eds) 27th IEEE International Requirements Engineering Conference, RE 2019, Jeju Island, Korea (South), September 23-27, 2019. IEEE, pp 363\u2013368, (2019). https:\/\/doi.org\/10.1109\/RE.2019.00046","DOI":"10.1109\/RE.2019.00046"},{"key":"507_CR34","doi-asserted-by":"crossref","unstructured":"Ladner, R.E., Reif, J.H.: The logic of distributed protocols. In: Halpern JY (ed) Proceedings of the 1st Conference on Theoretical Aspects of Reasoning about Knowledge, Monterey, CA, USA, March 1986. Morgan Kaufmann, pp 207\u2013222 (1986)","DOI":"10.1016\/B978-0-934613-04-0.50016-8"},{"key":"507_CR35","doi-asserted-by":"publisher","DOI":"10.1016\/j.artint.2021.103473","volume":"296","author":"M Langer","year":"2021","unstructured":"Langer, M., Oster, D., Speith, T., et al.: What do we want from explainable artificial intelligence (xai)? - a stakeholder perspective on xai and a conceptual model guiding interdisciplinary xai research. Artif. Intell. 296, 103473 (2021). https:\/\/doi.org\/10.1016\/j.artint.2021.103473","journal-title":"Artif. Intell."},{"key":"507_CR36","volume-title":"Counterfactuals","author":"DK Lewis","year":"1973","unstructured":"Lewis, D.K.: Counterfactuals. Blackwell, Cambridge, MA, USA (1973)"},{"key":"507_CR37","doi-asserted-by":"crossref","unstructured":"Lewis, D.K.: Causal explanation. In: Lewis D (ed) Philosophical Papers Vol. II. Oxford University Press, p 214\u2013240 (1986)","DOI":"10.1093\/0195036468.003.0007"},{"key":"507_CR38","doi-asserted-by":"publisher","unstructured":"Lichtenstein, O., Pnueli, A., Zuck, L.D.: The glory of the past. In: Parikh R (ed) Logics of Programs, Conference, Brooklyn College, New York, NY, USA, June 17-19, 1985, Proceedings, Lecture Notes in Computer Science, vol 193. Springer, pp 196\u2013218, (1985). https:\/\/doi.org\/10.1007\/3-540-15648-8_16","DOI":"10.1007\/3-540-15648-8_16"},{"issue":"2","key":"507_CR39","doi-asserted-by":"publisher","first-page":"485","DOI":"10.1093\/logcom\/exac102","volume":"33","author":"X Liu","year":"2023","unstructured":"Liu, X., Lorini, E.: A unified logical framework for explanations in classifier systems. J. Log. Comput. 33(2), 485\u2013515 (2023). https:\/\/doi.org\/10.1093\/logcom\/exac102","journal-title":"J. Log. Comput."},{"key":"507_CR40","doi-asserted-by":"publisher","unstructured":"van\u00a0der Meyden, R., Shilov, N.V.: Model checking knowledge and time in systems with perfect recall (extended abstract). In: Rangan,C.P., Raman, V., Ramanujam, R. (eds) Foundations of Software Technology and Theoretical Computer Science, 19th Conference, Chennai, India, December 13-15, 1999, Proceedings, Lecture Notes in Computer Science, vol 1738. Springer, pp 432\u2013445, (1999). https:\/\/doi.org\/10.1007\/3-540-46691-6_35","DOI":"10.1007\/3-540-46691-6_35"},{"key":"507_CR41","doi-asserted-by":"publisher","unstructured":"van\u00a0der Meyden, R., Su. K.: Symbolic model checking the knowledge of the dining cryptographers. In: 17th IEEE Computer Security Foundations Workshop, (CSFW-17 2004), 28-30 June 2004, Pacific Grove, CA, USA. IEEE Computer Society, p 280, (2004). https:\/\/doi.org\/10.1109\/CSFW.2004.19, https:\/\/doi.ieeecomputersociety.org\/10.1109\/CSFW.2004.19","DOI":"10.1109\/CSFW.2004.19"},{"key":"507_CR42","doi-asserted-by":"publisher","unstructured":"van\u00a0der Meyden, R., Vardi, M.Y.: Synthesis from knowledge-based specifications (extended abstract). In: Sangiorgi D, de\u00a0Simone R (eds) CONCUR \u201998: Concurrency Theory, 9th International Conference, Nice, France, September 8-11, 1998, Proceedings, Lecture Notes in Computer Science, vol 1466. Springer, pp 34\u201349, (1998). https:\/\/doi.org\/10.1007\/BFb0055614","DOI":"10.1007\/BFb0055614"},{"key":"507_CR43","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). https:\/\/doi.org\/10.1016\/j.artint.2018.07.007","journal-title":"Artif. Intell."},{"key":"507_CR44","doi-asserted-by":"publisher","unstructured":"Pnueli, A.: The temporal logic of programs. In: 18th Annual Symposium on Foundations of Computer Science, Providence, Rhode Island, USA, 31 October - 1 November 1977. IEEE Computer Society, pp 46\u201357, https:\/\/doi.org\/10.1109\/SFCS.1977.32","DOI":"10.1109\/SFCS.1977.32"},{"key":"507_CR45","doi-asserted-by":"publisher","unstructured":"Poyiadzi, R., Sokol, K., Santos-Rodr\u00edguez, R., et\u00a0al.: FACE: feasible and actionable counterfactual explanations. In: Markham AN, Powles J, Walsh T, et\u00a0al (eds) AIES \u201920: AAAI\/ACM Conference on AI, Ethics, and Society, New York, NY, USA, February 7-8, 2020. ACM, pp 344\u2013350, (2020). https:\/\/doi.org\/10.1145\/3375627.3375850","DOI":"10.1145\/3375627.3375850"},{"key":"507_CR46","unstructured":"Rabe, M.N.: A temporal logic approach to information-flow control. PhD thesis, Saarland University, (2016). http:\/\/scidok.sulb.uni-saarland.de\/volltexte\/2016\/6387\/"},{"issue":"6","key":"507_CR47","doi-asserted-by":"publisher","first-page":"673","DOI":"10.1007\/s10458-019-09408-y","volume":"33","author":"A Rosenfeld","year":"2019","unstructured":"Rosenfeld, A., Richardson, A.: Explainability in human-agent systems. Auton Agents Multi Agent Syst 33(6), 673\u2013705 (2019). https:\/\/doi.org\/10.1007\/s10458-019-09408-y","journal-title":"Auton Agents Multi Agent Syst"},{"key":"507_CR48","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1007\/978-3-030-91779-1_8","volume-title":"Deceptive AI","author":"C Sakama","year":"2021","unstructured":"Sakama, C.: Deception in epistemic causal logic. In: Sarkadi, S., Wright, B., Masters, P., et al. (eds.) Deceptive AI, pp. 105\u2013123. Springer International Publishing, Cham (2021)"},{"key":"507_CR49","unstructured":"Sandu, A.S.: Knowledge of counterfactuals. PhD thesis, Cornell University (2021)"},{"key":"507_CR50","doi-asserted-by":"publisher","DOI":"10.1016\/j.chb.2021.106837","volume":"122","author":"N Schlicker","year":"2021","unstructured":"Schlicker, N., Langer, M., \u00d6tting, S.K., et al.: What to expect from opening up \u2018black boxes\u2019? comparing perceptions of justice between human and automated agents. Comput. Hum. Behav. 122, 106837 (2021). https:\/\/doi.org\/10.1016\/j.chb.2021.106837","journal-title":"Comput. Hum. Behav."},{"key":"507_CR51","doi-asserted-by":"publisher","unstructured":"Stalnaker, R.: A Theory of Conditionals, Springer Netherlands, Dordrecht, pp 41\u201355, (1981). https:\/\/doi.org\/10.1007\/978-94-009-9117-0_2","DOI":"10.1007\/978-94-009-9117-0_2"},{"issue":"1","key":"507_CR52","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1007\/s11098-005-4062-y","volume":"128","author":"R Stalnaker","year":"2006","unstructured":"Stalnaker, R.: On logics of knowledge and belief. Philosophical Studies: An International Journal for Philosophy in the Analytic Tradition 128(1), 169\u2013199 (2006). (http:\/\/www.jstor.org\/stable\/4321718)","journal-title":"Philosophical Studies: An International Journal for Philosophy in the Analytic Tradition"},{"issue":"2","key":"507_CR53","first-page":"841","volume":"31","author":"S Wachter","year":"2018","unstructured":"Wachter, S., Mittelstadt, B., Russell, C.: Counterfactual explanations without opening the black box: automated decisions and the gdpr. Harvard Journal of Law and Technology 31(2), 841\u2013887 (2018)","journal-title":"Harvard Journal of Law and Technology"},{"issue":"3","key":"507_CR54","doi-asserted-by":"publisher","first-page":"347","DOI":"10.1007\/s11334-022-00452-8","volume":"18","author":"R Ziemek","year":"2022","unstructured":"Ziemek, R., Piribauer, J., Funke, F., et al.: Probabilistic causes in markov chains. Innov. Syst. Softw. Eng. 18(3), 347\u2013367 (2022). https:\/\/doi.org\/10.1007\/s11334-022-00452-8","journal-title":"Innov. Syst. Softw. Eng."}],"container-title":["Acta Informatica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00236-025-00507-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00236-025-00507-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00236-025-00507-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,12]],"date-time":"2025-12-12T09:14:38Z","timestamp":1765530878000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00236-025-00507-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,13]]},"references-count":54,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2025,12]]}},"alternative-id":["507"],"URL":"https:\/\/doi.org\/10.1007\/s00236-025-00507-w","relation":{},"ISSN":["0001-5903","1432-0525"],"issn-type":[{"value":"0001-5903","type":"print"},{"value":"1432-0525","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,10,13]]},"assertion":[{"value":"29 November 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 July 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 October 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"38"}}