2019/12/06 by Pietro Galliani, Galliani, Pietro, Jouko Väänánen +2
Computer Science · Mathematics · #03B70 #Advanced Algebra and Logic #F.4.1 #FOS: Computer and information sciences #FOS: Mathematics #Logic (math.LO) #Logic in Computer Science (cs.LO) #Logic, Reasoning, and Knowledge #Rough Sets and Fuzzy Logic #acm:03B70 #cs.LO #math.LO #msc:03B70
paper · pdf · doi:10.48550/arxiv.1912.03252
openalex publication_date 2019/12/06 · arxiv created 2021/09/24 · arxiv updated 2021/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the concepts of dependence and independence in a very general framework. We use a concept of rank to study dependence and independence. By means of the rank we identify (total) dependence with inability to create more diversity, and (total) 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.