{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:44:51Z","timestamp":1740123891180,"version":"3.37.3"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"2-3","license":[{"start":{"date-parts":[[2021,11,1]],"date-time":"2021-11-01T00:00:00Z","timestamp":1635724800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2021,11,1]],"date-time":"2021-11-01T00:00:00Z","timestamp":1635724800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100008815","name":"Libera Universit\u00e0 di Bolzano","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100008815","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Ann Math Artif Intell"],"published-print":{"date-parts":[[2022,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We propose a very general, unifying framework for the concepts of dependence and independence. For this purpose, we introduce the notion of <jats:italic>diversity rank<\/jats:italic>. By means of this diversity rank we identify <jats:italic>total determination<\/jats:italic> with the inability to create more diversity, and <jats:italic>independence<\/jats:italic> with the presence of maximum diversity. We show that our theory of dependence and independence covers a variety of dependence concepts, for example the seemingly unrelated concepts of linear dependence in algebra and dependence of variables in logic.<\/jats:p>","DOI":"10.1007\/s10472-021-09778-8","type":"journal-article","created":{"date-parts":[[2021,11,1]],"date-time":"2021-11-01T09:02:55Z","timestamp":1635757375000},"page":"211-233","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Diversity, dependence and independence"],"prefix":"10.1007","volume":"90","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2544-5332","authenticated-orcid":false,"given":"Pietro","family":"Galliani","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jouko","family":"V\u00e4\u00e4n\u00e4nen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,11,1]]},"reference":[{"issue":"3","key":"9778_CR1","doi-asserted-by":"publisher","first-page":"509","DOI":"10.2307\/2371182","volume":"57","author":"H Whitney","year":"1935","unstructured":"Whitney, H.: On the Abstract Properties of Linear Dependence. Amer. J. Math. 57(3), 509\u2013533 (1935). https:\/\/doi.org\/10.2307\/2371182","journal-title":"Amer. J. Math."},{"key":"9778_CR2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-41905-2","volume-title":"Moderne Algebra","author":"BL van der Waerden","year":"1940","unstructured":"van der Waerden, B.L.: Moderne Algebra. J. Springer, Berlin (1940)"},{"key":"9778_CR3","unstructured":"Armstrong, WW.: Dependency structures of data base relationships. Inf Process. 74 (1974)"},{"key":"9778_CR4","volume-title":"Dependence logic. London Mathematical Society Student Texts, vol. 70","author":"J V\u00e4\u00e4n\u00e4nen","year":"2007","unstructured":"V\u00e4\u00e4n\u00e4nen, J.: Dependence logic. London Mathematical Society Student Texts, vol. 70. Cambridge University Press, Cambridge (2007)"},{"key":"9778_CR5","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511981418","volume-title":"Independence-friendly logic. London Mathematical Society Lecture Note Series, vol. 386","author":"AL Mann","year":"2011","unstructured":"Mann, AL., Sandu, G., Sevenster, M.: Independence-friendly logic. London Mathematical Society Lecture Note Series, vol. 386. Cambridge University Press, Cambridge (2011). https:\/\/doi.org\/10.1017\/CBO9780511981418. A game-theoretic approach"},{"issue":"2","key":"9778_CR6","doi-asserted-by":"publisher","first-page":"399","DOI":"10.1007\/s11225-013-9479-2","volume":"101","author":"E Gr\u00e4del","year":"2013","unstructured":"Gr\u00e4del, E., V\u00e4\u00e4n\u00e4nen, J.: Dependence and independence. Studia Log. 101(2), 399\u2013410 (2013). https:\/\/doi.org\/10.1007\/s11225-013-9479-2","journal-title":"Studia Log."},{"issue":"7","key":"9778_CR7","doi-asserted-by":"publisher","first-page":"557","DOI":"10.1016\/j.apal.2016.03.003","volume":"167","author":"F Yang","year":"2016","unstructured":"Yang, F., V\u00e4\u00e4n\u00e4nen, J.: Propositional logics of dependence. Ann. Pure Appl. Log. 167(7), 557\u2013589 (2016)","journal-title":"Ann. Pure Appl. Log."},{"key":"9778_CR8","unstructured":"V\u00e4\u00e4n\u00e4nen, J.: Modal dependence logic. In: New perspectives on games and interaction, Texts in Logic and Games, vol. 4, pp 237\u2013254. Amsterdam Univ. Press, Amsterdam (2008)"},{"key":"9778_CR9","unstructured":"Hella, L., Luosto, K., Sano, K., Virtema, J.: The expressive power of modal dependence logic. In: Advances in modal logic. Vol. 10, pp 294\u2013312. Coll. Publ., London (2014)"},{"key":"9778_CR10","unstructured":"Krebs, A., Meier, A., Virtema, J., Zimmermann, M.: Team semantics for the specification and verification of hyperproperties. In: 43rd International Symposium on Mathematical Foundations of Computer Science, LIPIcs. Leibniz Int. Proc. Inform., vol. 117, pp 10\u201316. Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern (2018)"},{"issue":"5-6","key":"9778_CR11","doi-asserted-by":"publisher","first-page":"475","DOI":"10.1007\/s00153-017-0535-x","volume":"56","author":"T Hyttinen","year":"2017","unstructured":"Hyttinen, T., Paolini, G., V\u00e4\u00e4n\u00e4nen, J.: A logic for arguing about probabilities in measure teams. Arch. Math. Log. 56(5-6), 475\u2013489 (2017)","journal-title":"Arch. Math. Log."},{"key":"9778_CR12","doi-asserted-by":"publisher","unstructured":"Durand, A., Hannula, M., Kontinen, J., Meier, A., Virtema, J.: Probabilistic team semantics. In: Foundations of information and knowledge systems, Lecture Notes in Comput. Sci. https:\/\/doi.org\/10.1007\/978-3-319-90050-6_1, vol. 10833, pp 186\u2013206. Springer, Cham (2018)","DOI":"10.1007\/978-3-319-90050-6_1"},{"key":"9778_CR13","doi-asserted-by":"publisher","unstructured":"Hannula, M., Hirvonen, \u00c5., Kontinen, J., Kulikov, V., Virtema, J.: Facets of distribution identities in probabilistic team semantics. In: Logics in artificial intelligence, Lecture Notes in Comput. Sci. https:\/\/doi.org\/10.1007\/978-3-030-19570-0_2, vol. 11468, pp 304\u2013320. Springer, Cham (2019)","DOI":"10.1007\/978-3-030-19570-0_2"},{"key":"9778_CR14","volume-title":"Matroid theory, vol. 3","author":"JG Oxley","year":"2006","unstructured":"Oxley, J.G.: Matroid theory, vol. 3. Oxford University Press, USA (2006)"},{"issue":"3\/4","key":"9778_CR15","doi-asserted-by":"publisher","first-page":"237","DOI":"10.2307\/2333344","volume":"40","author":"IJ Good","year":"1953","unstructured":"Good, I.J.: The population frequencies of species and the estimation of population parameters. Biometrika 40(3\/4), 237\u2013264 (1953)","journal-title":"Biometrika"},{"key":"9778_CR16","doi-asserted-by":"publisher","first-page":"427","DOI":"10.2307\/1934352","volume":"54","author":"M Hill","year":"1973","unstructured":"Hill, M.: Diversity and evenness: A unifying notation and its consequences. Ecology 54, 427\u2013432 (1973). https:\/\/doi.org\/10.2307\/1934352","journal-title":"Ecology"},{"key":"9778_CR17","volume-title":"Measuring biological diversity","author":"AE Magurran","year":"2004","unstructured":"Magurran, A.E.: Measuring biological diversity. Wiley, New Jersey (2004). https:\/\/books.google.fi\/books?id=tUqzLSUzXxcC"},{"key":"9778_CR18","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-20347-3","volume-title":"Fundamentals in information theory and coding","author":"M Borda","year":"2011","unstructured":"Borda, M.: Fundamentals in information theory and coding. Springer Science & Business Media, Berlin (2011)"},{"key":"9778_CR19","first-page":"1","volume":"2","author":"TM Cover","year":"1991","unstructured":"Cover, T.M., Thomas, J.A.: Entropy, relative entropy and mutual information. Elem. Inf. Theory 2, 1\u201355 (1991)","journal-title":"Elem. Inf. Theory"},{"issue":"1","key":"9778_CR20","doi-asserted-by":"publisher","first-page":"128","DOI":"10.1016\/0890-5401(91)90077-F","volume":"91","author":"D Geiger","year":"1991","unstructured":"Geiger, D., Paz, A., Pearl, J.: Axioms and algorithms for inferences involving probabilistic independence. Inform. and Comput. 91(1), 128\u2013141 (1991). https:\/\/doi.org\/10.1016\/0890-5401(91)90077-F","journal-title":"Inform. and Comput."},{"issue":"3","key":"9778_CR21","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","volume":"27","author":"CE Shannon","year":"1948","unstructured":"Shannon, C.E.: A mathematical theory of communication. Bell syst. Techn. J. 27(3), 379\u2013423 (1948)","journal-title":"Bell syst. Techn. J."},{"key":"9778_CR22","doi-asserted-by":"crossref","unstructured":"Codd, E.F.: A relational model of data for large shared data banks communications. Commun. ACM 26(1) (1970)","DOI":"10.1145\/357980.358007"},{"key":"9778_CR23","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-0041-0","volume-title":"Algebra","author":"S Lang","year":"2002","unstructured":"Lang, S., et al.: Algebra. Springer, Berlin (2002)"},{"issue":"2","key":"9778_CR24","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1006\/inco.1995.1148","volume":"122","author":"C Herrmann","year":"1995","unstructured":"Herrmann, C.: On the undecidability of implications between embedded multivalued database dependencies. Inf. Comput. 122(2), 221\u2013235 (1995)","journal-title":"Inf. Comput."},{"issue":"12","key":"9778_CR25","doi-asserted-by":"publisher","first-page":"1847","DOI":"10.1016\/j.ic.2006.09.002","volume":"204","author":"C Herrmann","year":"2006","unstructured":"Herrmann, C.: Corrigendum to: On the undecidability of implications between embedded multivalued database dependencies. Inform. and Comput. 204 (12), 1847\u20131851 (2006)","journal-title":"Inform. and Comput."},{"key":"9778_CR26","doi-asserted-by":"crossref","unstructured":"Hannula, M., Link, S.: On the interaction of functional and inclusion dependencies with independence atoms. In: International Conference on Database Systems for Advanced Applications, pp 353\u2013369, Springer (2018)","DOI":"10.1007\/978-3-319-91458-9_21"},{"key":"9778_CR27","volume-title":"A Decision Method for Elementary Algebra and Geometry","author":"A Tarski","year":"1948","unstructured":"Tarski, A.: A Decision Method for Elementary Algebra and Geometry. RAND Corporation, Santa Monica (1948)"},{"issue":"2","key":"9778_CR28","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1016\/j.is.2007.07.005","volume":"33","author":"B Sayrafi","year":"2008","unstructured":"Sayrafi, B., Van Gucht, D., Gyssens, M.: The implication problem for measure-based constraints. Inf. Syst. 33(2), 221\u2013239 (2008)","journal-title":"Inf. Syst."},{"key":"9778_CR29","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1016\/j.artint.2013.06.005","volume":"202","author":"M Niepert","year":"2013","unstructured":"Niepert, M., Gyssens, M., Sayrafi, B., Van Gucht, D.: On the conditional independence implication problem: A lattice-theoretic approach. Artif. Intell. 202, 29\u201351 (2013)","journal-title":"Artif. Intell."}],"container-title":["Annals of Mathematics and Artificial Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10472-021-09778-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10472-021-09778-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10472-021-09778-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,1,31]],"date-time":"2022-01-31T02:06:35Z","timestamp":1643594795000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10472-021-09778-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,1]]},"references-count":29,"journal-issue":{"issue":"2-3","published-print":{"date-parts":[[2022,3]]}},"alternative-id":["9778"],"URL":"https:\/\/doi.org\/10.1007\/s10472-021-09778-8","relation":{},"ISSN":["1012-2443","1573-7470"],"issn-type":[{"type":"print","value":"1012-2443"},{"type":"electronic","value":"1573-7470"}],"subject":[],"published":{"date-parts":[[2021,11,1]]},"assertion":[{"value":"4 October 2021","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 November 2021","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}