2014/09/12 by João Pita Costa, Costa, João Pita, Primož Škraba +4
Computer Science · Mathematics · Medicine · #03G10 #Alzheimer's disease research and treatments #Computational Geometry (cs.CG) #FOS: Computer and information sciences #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #Rings and Algebras (math.RA) #Topological and Geometric Data Analysis #cs.CG #math.LO #math.RA #msc:03G10
paper · pdf · doi:10.48550/arxiv.1409.3762
openalex publication_date 2014/09/12 · arxiv created 2014/09/15 · arxiv updated 2014/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The foundational character of certain algebraic structures as Boolean algebras and Heyting algebras is rooted in their potential to model classical and constructive logic, respectively. In this paper we discuss the contributions of algebraic logic to the study of persistence based on a new operation on the ordered structure of the input diagram of vector spaces and linear maps given by a filtration. Within the context of persistence theory, we give an analysis of the underlying algebra, derive universal properties and discuss new applications. We highlight the definition of the implication operation within this construction, as well as interpret its meaning within persistent homology, multidimensional persistence and zig-zag persistence.