Modal structures in groups and vector spaces
Johan van Benthem, Nick Bezhanishvili

Abstract:
Vector spaces show a number of general structures that invite analysis in modal logics.
As such, they provide an interesting counterpart to the much better-studied modal logics of topology. At the same time, vector spaces pose several challenges to this style of analysis of a mathematical practice. In this programmatic paper, we present a number of modal logics of groups and then full fledged vector spaces, including some new logics of dependence and independence. In particular, we investigate issues of definability and axiomatization using standard techniques for modal and hybrid languages. Our discussion identifies several leads for more systematic research.