A logic for n-dimensional hierarchical refinement
  Hierarchical transition systems provide a popular mathematical structure to represent state-based software applications in which different layers of abstraction are represented by inter-related state machines. The decomposition of high level states into inner sub-states, and of their transitions into inner sub-transitions is common refinement procedure adopted in a number of specification formalisms.   This paper introduces a hybrid modal logic for k-layered transition systems, its first-order standard translation, a notion of bisimulation, and a modal invariance result. Layered and hierarchical notions of refinement are also discussed in this setting. 
Alexandre Madeira (HASLab INESC TEC and Universidade do Minho), Manuel   A. Martins (CIDMA and Dep Matem\'atica Universidade...
cs.LO cs.SE