We present a modal logic for describing the spatial organization and the behavior of distributed systems. In addition to standard logical and temporal operators, our logic includes spatial operations corresponding to process composition and name hiding, and a fresh name quantifier. In Part I of this work we study the fundamental semantic properties of our logic; the focus of the present Part II is on proof theory. The main contributions are a sequent-based proof system for our logic, and a proof of cut-elimination for its first-order fragment.
