Abstract
AbstractWe propose a very general, unifying framework for the concepts of dependence and independence. For this purpose, we introduce the notion of diversity rank. By means of this diversity rank we identify total determination with the inability to create more diversity, and independence 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.
Funder
Libera Università di Bolzano
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Artificial Intelligence
Reference29 articles.
1. Whitney, H.: On the Abstract Properties of Linear Dependence. Amer. J. Math. 57(3), 509–533 (1935). https://doi.org/10.2307/2371182
2. van der Waerden, B.L.: Moderne Algebra. J. Springer, Berlin (1940)
3. Armstrong, WW.: Dependency structures of data base relationships. Inf Process. 74 (1974)
4. Väänänen, J.: Dependence logic. London Mathematical Society Student Texts, vol. 70. Cambridge University Press, Cambridge (2007)
5. 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