Constructive processes (i.e., derivations which gradually build up a model of the world) play an important role in the area of knowledge representation. We study such processes in an algebraic way, which proves to be a convenient way of deriving general theorems about different knowledge representation languages. Moreover, we also investigate the relation between constructive processes and causality. We observe that causal statements are essentially dynamic statements, which makes it natural to formalize their meaning in terms of constructive processes. Based on this observation, we develop the formal language of CP-logic as a new way of representing causal probabilistic knowledge.