Active integrity constraints have been introduced in the database community as a way to restore integrity based on a set of preferred update actions. We view active integrity constraints as dynamic logic programs and show how several semantics of database repair that were proposed in the literature can be characterised in Dynamic Logic of Propositional Assignments DL-PA. We moreover propose a new definition of repair which makes use of the programs of Dynamic Logic to provide repair solutions based on an iterating procedure. After an analysis of their properties and a comparison to the previous approaches, we provide complexity results for the problem of existence of these new repairs. Furthermore, an extension on databases with history is explored and the behavior of the various repairs is adjusted to work in this setting. For all these definitions we provide DL-PA counterparts of reasoning and decision problems, such as the existence of a repair or the existence of a unique repair.