Differential dynamic logic ($$d\mathcal {L}$$dL) is a dynamic logic with first-order features which allows us to describe and reason about hybrid systems. We have already used this logic to reason about biological models. Here we explore some variants of its semantics in order to obtain a simplified and more intuitive way of describing errors/perturbations, unavoidable in real-case scenarios. More specifically, we introduce interval differential dynamic logic which takes $$d\mathcal {L}$$dL as its base and adapts its semantics for the interval setting.