Abstract
In this paper, we overview the recently introduced general framework of Description Logic Based Dynamic Systems, which leverages Levesque's functional approach to model systems that evolve the extensional part of a description logic knowledge base by means of actions. This framework is parametric w.r.t. the adopted description logic and the progression mechanism. In this setting, we discuss verification and adversarial synthesis for specifications expressed in a variant of first-order μ-calculus, with a controlled form of quantification across successive states and present key decidability results under the natural assumption of state-boundedness.