METRICS FOR FORMAL STRUCTURES, WITH AN APPLICATION TO KRIPKE MODELS AND THEIR DYNAMICS

Abstract The paper introduces a broad family of metrics applicable to finite and countably infinite strings, or, by extension, formal structures serving as semantics for countable languages. main focus is on applications sets pointed Kripke models, modal logics. For the resulting metric spaces, classifies topological properties including which are topologically equivalent, providing sufficient conditions compactness, characterizing clopen isolated points, metrical topologies concept logical convergence. We then apply approach maps from dynamic epistemic logic, showing that product updates with action models yield continuous maps, hence allowing an interpretation iterated discrete time dynamical systems.