A logic for Persistence

A new paper on the Persistence Lattice was just made available during the CCC2014 conference, this year in Ljubljana. The paper Aspects of an internal logic for persistence, available at the arXiv 1409.3762, discusses 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. This is a collaborative work of João Pita Costa, Primož Škraba, and Mikael Vejdemo-Johansson.