{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,1]],"date-time":"2025-07-01T04:05:04Z","timestamp":1751342704352,"version":"3.37.3"},"reference-count":56,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2023,3,23]],"date-time":"2023-03-23T00:00:00Z","timestamp":1679529600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,3,23]],"date-time":"2023-03-23T00:00:00Z","timestamp":1679529600000},"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":["Ann Math Artif Intell"],"published-print":{"date-parts":[[2024,1]]},"DOI":"10.1007\/s10472-023-09833-6","type":"journal-article","created":{"date-parts":[[2023,3,23]],"date-time":"2023-03-23T07:04:09Z","timestamp":1679555049000},"page":"29-47","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Galois theory for analogical classifiers"],"prefix":"10.1007","volume":"92","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2316-7623","authenticated-orcid":false,"given":"Miguel","family":"Couceiro","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Erkko","family":"Lehtonen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,3,23]]},"reference":[{"key":"9833_CR1","doi-asserted-by":"crossref","unstructured":"Alsaidi, S., Decker, A., Lay, P., Marquer, E., Murena, P.-A., Couceiro, M.: A neural approach for detecting morphological analogies. In: IEEE DSAA 2021, pp. 1\u201310 (2021)","DOI":"10.1109\/DSAA53316.2021.9564186"},{"key":"9833_CR2","unstructured":"Fahandar, M.A., H\u00fcllermeier, E.: Learning to rank based on analogical reasoning. In: AAAI-18, pp. 2951\u20132958 (2018)"},{"key":"9833_CR3","doi-asserted-by":"crossref","unstructured":"Fahandar, M.A., H\u00fcllermeier, E.: Analogical embedding for analogy-based learning to rank. In: IDA 2021. LNCS, vol. 12695, pp 76\u201388. Springer (2021)","DOI":"10.1007\/978-3-030-74251-5_7"},{"key":"9833_CR4","doi-asserted-by":"crossref","unstructured":"Mitchell, M.: Abstraction and analogy-making in artificial intelligence. arXiv:2102.10717 (2021)","DOI":"10.1162\/isal_a_00354"},{"key":"9833_CR5","unstructured":"Sadeghi, F., Zitnick, C.L., Farhadi, A.: Visalogy: Answering visual analogy questions. In: NIPS 2015, pp. 1882\u20131890 (2015)"},{"key":"9833_CR6","doi-asserted-by":"crossref","unstructured":"Peyre, J., Laptev, I., Schmid, C., Sivic, J.: Detecting unseen visual relations using analogies. In: IEEE ICCV 2019, pp. 1981\u20131990 (2019)","DOI":"10.1109\/ICCV.2019.00207"},{"key":"9833_CR7","doi-asserted-by":"crossref","unstructured":"Couceiro, M., Hug, N., Prade, H., Richard, G.: Analogy-preserving functions: A way to extend Boolean samples. In: IJCAI. ijcai.org, pp 1575\u20131581 (2017)","DOI":"10.24963\/ijcai.2017\/218"},{"key":"9833_CR8","doi-asserted-by":"crossref","unstructured":"Cornu\u00e9jols, A., Murena, P.-A., Olivier, R.: Transfer learning by learning projections from target to source. In: IDA 2020. LNCS, vol. 12080, pp. 119\u2013131. Springer (2020)","DOI":"10.1007\/978-3-030-44584-3_10"},{"key":"9833_CR9","doi-asserted-by":"crossref","unstructured":"Alsaidi, S., Decker, A., Lay, P., Marquer, E., Murena, P.-A., Couceiro, M.: On the transferability of neural models of morphological analogies. In: AIMLAI@ECML\/PKDD, pp 76\u201389 (2021)","DOI":"10.1007\/978-3-030-93736-2_7"},{"key":"9833_CR10","doi-asserted-by":"crossref","unstructured":"H\u00fcllermeier, E.: Towards analogy-based explanations in machine learning. In: MDAI 2020. LNCS, vol. 12256, pp. 205\u2013217. Springer (2020)","DOI":"10.1007\/978-3-030-57524-3_17"},{"key":"9833_CR11","doi-asserted-by":"crossref","unstructured":"Keane, M.T., Smyth, B.: Good counterfactuals and where to find them: a case-based technique for generating counterfactuals for explainable AI (XAI). In: ICCBR 2020. LNCS, vol. 12311, pp. 163\u2013178. Springer (2020)","DOI":"10.1007\/978-3-030-58342-2_11"},{"key":"9833_CR12","doi-asserted-by":"publisher","first-page":"180","DOI":"10.1016\/S1571-0661(05)82582-4","volume":"53","author":"Y Lepage","year":"2001","unstructured":"Lepage, Y.: Analogy and formal languages. Electron. Notes Theor. Comput. Sci. 53, 180\u2013191 (2001)","journal-title":"Electron. Notes Theor. Comput. Sci."},{"key":"9833_CR13","doi-asserted-by":"publisher","first-page":"793","DOI":"10.1613\/jair.2519","volume":"32","author":"L Miclet","year":"2008","unstructured":"Miclet, L., Bayoudh, S., Delhay, A.: Analogical dissimilarity: definition, algorithms and two experiments in machine learning. J. Artif. Intell. Res. 32, 793\u2013824 (2008)","journal-title":"J. Artif. Intell. Res."},{"key":"9833_CR14","unstructured":"Lepage, Y.: De l\u2019analogie rendant compte de la communication en linguistique. https:\/\/tel.archives-ouvertes.fr\/tel-00004372 (2003)"},{"key":"9833_CR15","volume-title":"Case-based Reasoning","author":"MM Richter","year":"2016","unstructured":"Richter, M.M., Weber, R.O.: Case-based Reasoning. Springer, Berlin (2016)"},{"key":"9833_CR16","doi-asserted-by":"crossref","unstructured":"Lieber, J., Nauer, E., Prade, H.: When revision-based case adaptation meets analogical extrapolation. In: ICCBR 2021. LNCS, vol. 12877, pp. 156\u2013170. Springer (2021)","DOI":"10.1007\/978-3-030-86957-1_11"},{"key":"9833_CR17","first-page":"36","volume":"91","author":"M Bounhas","year":"2017","unstructured":"Bounhas, M., Prade, H., Richard, G.: Analogy-based classifiers for nominal or numerical data. IJAR 91, 36\u201355 (2017)","journal-title":"IJAR"},{"key":"9833_CR18","doi-asserted-by":"crossref","unstructured":"Couceiro, M., Hug, N., Prade, H., Richard, G.: Behavior of analogical inference w.r.t. Boolean functions. In: IJCAI. ijcai.org, pp 2057\u20132063 (2018)","DOI":"10.24963\/ijcai.2018\/284"},{"key":"9833_CR19","doi-asserted-by":"crossref","unstructured":"Couceiro, M., Lehtonen, E., Miclet, L., Prade, H., Richard, G.: When nominal analogical proportions do not fail. In: SUM 2020,. LNCS, vol. 12322, pp. 68\u201383. Springer (2020)","DOI":"10.1007\/978-3-030-58449-8_5"},{"issue":"4","key":"9833_CR20","doi-asserted-by":"publisher","first-page":"441","DOI":"10.1007\/s11787-013-0089-6","volume":"7","author":"H Prade","year":"2013","unstructured":"Prade, H., Richard, G.: From analogical proportion to logical proportions. Log. Univers. 7(4), 441\u2013505 (2013)","journal-title":"Log. Univers."},{"issue":"3","key":"9833_CR21","first-page":"1","volume":"5","author":"VG Bodnarchuk","year":"1969","unstructured":"Bodnarchuk, V.G., Kaluzhnin, L.A., Kotov, V.N., Romov, B.A.: Galois theory for Post algebras I. Kibernetika 5(3), 1\u201310 (1969)","journal-title":"Kibernetika"},{"issue":"5","key":"9833_CR22","first-page":"1","volume":"5","author":"VG Bodnarchuk","year":"1969","unstructured":"Bodnarchuk, V.G., Kaluzhnin, L.A., Kotov, V.N., Romov, B.A.: Galois theory for Post algebras II. Kibernetika 5(5), 1\u20139 (1969)","journal-title":"Kibernetika"},{"key":"9833_CR23","doi-asserted-by":"publisher","first-page":"95","DOI":"10.2140\/pjm.1968.27.95","volume":"27","author":"D Geiger","year":"1968","unstructured":"Geiger, D.: Closed systems of functions and predicates. Pacific J. Math. 27, 95\u2013100 (1968)","journal-title":"Pacific J. Math."},{"key":"9833_CR24","first-page":"175","volume":"40","author":"L Szab\u00f3","year":"1978","unstructured":"Szab\u00f3, L.: Concrete representation of related structures of universal algebras. I. Acta Sci. Math. (Szeged) 40, 175\u2013184 (1978)","journal-title":"I. Acta Sci. Math. (Szeged)"},{"key":"9833_CR25","unstructured":"P\u00f6schel, R.: Concrete representation of algebraic structures and a general Galois theory. In: Contributions to General Algebra 1, pp. 249\u2013272, Verlag Johannes Heyn (1979)"},{"issue":"1-3","key":"9833_CR26","doi-asserted-by":"publisher","first-page":"405","DOI":"10.1016\/S0012-365X(01)00297-7","volume":"254","author":"N Pippenger","year":"2002","unstructured":"Pippenger, N.: Galois theory for minors of finite functions. Discrete Math. 254(1-3), 405\u2013419 (2002)","journal-title":"Discrete Math."},{"key":"9833_CR27","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1007\/s00012-005-1933-1","volume":"54","author":"M Couceiro","year":"2005","unstructured":"Couceiro, M., Foldes, S.: On closed sets of relational constraints and classes of functions closed under variable substitutions. Algebra Universalis 54, 149\u2013165 (2005)","journal-title":"Algebra Universalis"},{"issue":"1-2","key":"9833_CR28","first-page":"15","volume":"72","author":"M Couceiro","year":"2006","unstructured":"Couceiro, M.: On Galois connections between external operations and relational constraints: arity restrictions and operator decompositions. Acta Sci. Math. 72(1-2), 15\u201335 (2006)","journal-title":"Acta Sci. Math."},{"issue":"1-3","key":"9833_CR29","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1016\/j.dam.2003.09.002","volume":"142","author":"M Couceiro","year":"2004","unstructured":"Couceiro, M., Foldes, S.: Definability of Boolean function classes by linear equations over GF(2). Discrete Appl. Math. 142(1-3), 29\u201334 (2004)","journal-title":"Discrete Appl. Math."},{"key":"9833_CR30","doi-asserted-by":"publisher","unstructured":"Couceiro, M., Lehtonen, E.: Stability of Boolean function classes with respect to clones of linear functions. Order. https:\/\/doi.org\/10.1007\/s11083-022-09596-5 (2023)","DOI":"10.1007\/s11083-022-09596-5"},{"issue":"2","key":"9833_CR31","doi-asserted-by":"publisher","first-page":"109","DOI":"10.7151\/dmgaa.1153","volume":"29","author":"M Couceiro","year":"2009","unstructured":"Couceiro, M., Foldes, S.: Function classes and relational constraints stable under compositions with clones. Discuss. Math. Gen. Algebra Appl. 29 (2), 109\u2013121 (2009)","journal-title":"Discuss. Math. Gen. Algebra Appl."},{"issue":"3","key":"9833_CR32","first-page":"457","volume":"3","author":"E Lehtonen","year":"2010","unstructured":"Lehtonen, E.: Characterization of preclones by matrix collections. Asian-Eur. J. Math. 3(3), 457\u2013473 (2010)","journal-title":"J. Math."},{"issue":"2-3","key":"9833_CR33","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1007\/s00012-010-0071-6","volume":"63","author":"E Lehtonen","year":"2010","unstructured":"Lehtonen, E.: Closed classes of functions, generalized constraints, and clusters. Algebra Universalis 63(2-3), 203\u2013234 (2010)","journal-title":"Algebra Universalis"},{"issue":"3","key":"9833_CR34","doi-asserted-by":"publisher","first-page":"273","DOI":"10.1007\/s00012-012-0184-1","volume":"67","author":"M Couceiro","year":"2012","unstructured":"Couceiro, M., Lehtonen, E.: Galois theory for sets of operations closed under permutation, cylindrification, and composition. Algebra Universalis 67(3), 273\u2013297 (2012)","journal-title":"Algebra Universalis"},{"key":"9833_CR35","unstructured":"De Saussure, F.: Cours de Linguistique G\u00e9n\u00e9rale, Lausanne \u2013 Paris Payot (1st edition) (1916)"},{"key":"9833_CR36","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.ijar.2021.02.002","volume":"132","author":"S Lim","year":"2021","unstructured":"Lim, S., Prade, H., Richard, G.: Classifying and completing word analogies by machine learning. Internat. J. Approx. Reason. 132, 1\u201325 (2021)","journal-title":"Internat. J. Approx. Reason."},{"issue":"6","key":"9833_CR37","doi-asserted-by":"publisher","first-page":"595","DOI":"10.1007\/s10472-022-09798-y","volume":"90","author":"C Anti\u0107","year":"2022","unstructured":"Anti\u0107, C.: Analogical proportions. Ann. Math. Artif. Intell. 90(6), 595\u2013644 (2022)","journal-title":"Ann. Math. Artif. Intell."},{"key":"9833_CR38","doi-asserted-by":"crossref","unstructured":"Murena, P.-A., Cornu\u00e9jols, A., Dessalles, J.-L.: Opening the parallelogram: Considerations on non-Euclidean analogies. In: ICCBR, pp 597\u2013611. Springer (2018)","DOI":"10.1007\/978-3-030-01081-2_39"},{"key":"9833_CR39","doi-asserted-by":"crossref","unstructured":"Stroppa, N., Yvon, F.: An analogical learner for morphological analysis. In: CoNLL 2005, ACL, pp. 120\u2013127 (2005)","DOI":"10.3115\/1706543.1706565"},{"key":"9833_CR40","doi-asserted-by":"publisher","first-page":"487","DOI":"10.1016\/j.artint.2019.06.008","volume":"275","author":"N Barbot","year":"2019","unstructured":"Barbot, N., Miclet, L., Prade, H.: Analogy between concepts. Artif. Intell. 275, 487\u2013539 (2019)","journal-title":"Artif. Intell."},{"key":"9833_CR41","doi-asserted-by":"crossref","unstructured":"Murena, P. -A., Al-Ghossein, M., Dessalles, J. -L., Cornu\u00e9jols, A.: Solving analogies on words based on minimal complexity transformation. In: IJCAI, pp. 1848\u20131854 (2020)","DOI":"10.24963\/ijcai.2020\/256"},{"issue":"3","key":"9833_CR42","doi-asserted-by":"publisher","first-page":"672","DOI":"10.1111\/tops.12278","volume":"9","author":"D Gentner","year":"2017","unstructured":"Gentner, D., Hoyos, C.: Analogy and abstraction. Top. Cogn. Sci. 9(3), 672\u2013693 (2017)","journal-title":"Top. Cogn. Sci."},{"issue":"1","key":"9833_CR43","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0004-3702(89)90077-5","volume":"41","author":"B Falkenhainer","year":"1989","unstructured":"Falkenhainer, B., Forbus, K.D., Gentner, D.: The structure-mapping engine: Algorithm and examples. Artif. Intell. 41(1), 1\u201363 (1989)","journal-title":"Artif. Intell."},{"key":"9833_CR44","doi-asserted-by":"crossref","unstructured":"Afantenos, S.D., Kunze, T., Lim, S., Prade, H., Richard, G.: Analogies between sentences: Theoretical aspects \u2013 preliminary experiments. In: ECSQARU 2021, pp. 3\u201318 (2021)","DOI":"10.1007\/978-3-030-86772-0_1"},{"key":"9833_CR45","doi-asserted-by":"crossref","unstructured":"Miclet, L., Prade, H.: Handling analogical proportions in classical logic and fuzzy logics settings. In: ECSQARU 2009, pp 638\u2013650. Springer, Berlin (2009)","DOI":"10.1007\/978-3-642-02906-6_55"},{"key":"9833_CR46","unstructured":"Klein, S.: Culture, mysticism & social structure and the calculation of behavior. In: ECAI 1982, pp. 141\u2013146 (1982)"},{"key":"9833_CR47","first-page":"3","volume":"10","author":"GA Burle","year":"1967","unstructured":"Burle, G.A.: Classes of k-valued logic which contain all functions of a single variable. Diskret. Analiz, Novosibirsk 10, 3\u20137 (1967)","journal-title":"Diskret. Analiz, Novosibirsk"},{"key":"9833_CR48","unstructured":"Anti\u0107, C.: Boolean proportions. arXiv:2109.00388v1 (2021)"},{"key":"9833_CR49","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1007\/s11083-006-9036-y","volume":"23","author":"E Lehtonen","year":"2006","unstructured":"Lehtonen, E.: Descending chains and antichains of the unary, linear, and monotone subfunction relations. Order 23, 129\u2013142 (2006)","journal-title":"Order"},{"issue":"8","key":"9833_CR50","doi-asserted-by":"publisher","first-page":"1981","DOI":"10.1016\/j.ejc.2010.05.007","volume":"31","author":"E Lehtonen","year":"2010","unstructured":"Lehtonen, E., Ne\u0161et\u0159il, J.: Minors of Boolean functions with respect to clique functions and hypergraph homomorphisms. European J. Combin. 31(8), 1981\u20131995 (2010)","journal-title":"European J. Combin."},{"key":"9833_CR51","unstructured":"Lehtonen, E., Szendrei, \u00c1.: Partial orders induced by quasilinear clones. In: Contributions to General Algebra 20, pp. 51\u201384. Verlag Johannes Heyn (2012)"},{"issue":"4","key":"9833_CR52","doi-asserted-by":"publisher","first-page":"673","DOI":"10.1016\/j.disc.2008.01.003","volume":"309","author":"E Lehtonen","year":"2009","unstructured":"Lehtonen, E., Szendrei, \u00c1.: Equivalence of operations with respect to discriminator clones. Discrete Math. 309(4), 673\u2013685 (2009)","journal-title":"Discrete Math."},{"issue":"2","key":"9833_CR53","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1007\/s00012-011-0120-9","volume":"65","author":"E Lehtonen","year":"2011","unstructured":"Lehtonen, E., Szendrei, \u00c1.: Clones with finitely many relative $\\mathcal {R}$-classes. Algebra Universalis 65(2), 109\u2013159 (2011)","journal-title":"Algebra Universalis"},{"issue":"1","key":"9833_CR54","doi-asserted-by":"publisher","first-page":"7","DOI":"10.7151\/dmgaa.1160","volume":"30","author":"E Lehtonen","year":"2010","unstructured":"Lehtonen, E., Szendrei, \u00c1.: The submaximal clones on the three-element set with finitely many relative $\\mathcal {R}$-classes. Discuss. Math. Gen. Algebra Appl. 30(1), 7\u201333 (2010)","journal-title":"Discuss. Math. Gen. Algebra Appl."},{"key":"9833_CR55","doi-asserted-by":"publisher","first-page":"200","DOI":"10.1016\/j.dam.2004.06.028","volume":"149","author":"I Zverovich","year":"2005","unstructured":"Zverovich, I.: Characterizations of closed classes of Boolean functions in terms of forbidden subfunctions and Post classes. Discrete Appl. Math. 149, 200\u2013218 (2005)","journal-title":"Discrete Appl. Math."},{"issue":"1","key":"9833_CR56","first-page":"1","volume":"1","author":"H Prade","year":"2014","unstructured":"Prade, H., Richard, G.: Homogenous and heterogeneous logical proportions. IfCoLog J. Logics Appl. 1(1), 1\u201352 (2014)","journal-title":"IfCoLog J. Logics Appl."}],"container-title":["Annals of Mathematics and Artificial Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10472-023-09833-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10472-023-09833-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10472-023-09833-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,5]],"date-time":"2024-02-05T03:13:39Z","timestamp":1707102819000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10472-023-09833-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,3,23]]},"references-count":56,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,1]]}},"alternative-id":["9833"],"URL":"https:\/\/doi.org\/10.1007\/s10472-023-09833-6","relation":{},"ISSN":["1012-2443","1573-7470"],"issn-type":[{"type":"print","value":"1012-2443"},{"type":"electronic","value":"1573-7470"}],"subject":[],"published":{"date-parts":[[2023,3,23]]},"assertion":[{"value":"13 January 2023","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 March 2023","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors have no competing interests to declare that are relevant to the content of this article.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"<!--Emphasis Type='Bold' removed-->Conflict of Interests"}}]}}