We extend hybrid dynamic logic with binders (for state variables) by distinguishing between observable and silent transitions. This differentiation gives rise to two kinds of observational interpretations: The first one relies on observational abstraction from the ordinary model class of a specification Sp by considering its closure under weak bisimulation. The second one uses an observational satisfaction relation for the axioms of the specification Sp, which relaxes the interpretation of state variables and the satisfaction of modal formulæ by abstracting from silent transitions. We establish a formal relationship between both approaches and show that they are equivalent under mild conditions. For the proof we instantiate the previously introduced concept of a behaviour-abstractor framework to the case of dynamic logic with binders and silent transitions. As a particular outcome we provide an invariance theorem and show the Hennessy-Milner property for weakly bisimilar labelled transition systems and observational satisfaction. In the second part of the paper we integrate our results in a development methodology for reactive systems leading to two versions of observational refinement. We provide conditions under which both kinds of refinement are semantically equivalent, involving implementation constructors for relabelling, hiding, and parallel composition.

通过区分可观察到的转换和静默转换，我们用粘合剂（用于状态变量）扩展了混合动态逻辑。这种差异产生了两种观察性解释：第一种依赖于从规范Sp的普通模型类的观察抽象，通过考虑弱互模拟下的闭包。第二个使用观测满足关系作为规范Sp的公理，通过从静默转换中抽象出来，放宽了状态变量的解释和模态公式的满足。我们在两种方法之间建立了正式关系，并表明它们在温和条件下是等效的。为了证明，我们将先前引入的行为抽象器框架概念实例化为具有绑定器和静默转换的动态逻辑的情况。作为一个特殊的结果，我们提供了一个不变性定理，并展示了弱双相似标记转换系统和观察满意度的 Hennessy-Milner 特性。在论文的第二部分，我们将我们的结果整合到反应系统的开发方法中，从而导致两个版本的观察改进。我们提供了两种细化在语义上等效的条件，