A simple model of dynamic databases is studied from a modal logic perspecitve. A state $$\alpha$$ of a database is an atomic update of a state $$\beta$$ if at most one atomic statement is evaluated differently in $$\alpha$$ compared to $$\beta$$. The corresponding restriction on Kripke-like structures yields so-called update logics. These logics are studied also in a many-valued context. Adequate tableau calculi are given.