Abstraction is a commonly used process to represent some low-level system by a more coarse specification with the goal to omit unnecessary details while preserving important aspects. While recent work on abstraction in the situation calculus has focused on non-probabilistic domains, we describe an approach to abstraction of probabilistic and dynamic systems. Based on a variant of the situation calculus with probabilistic belief, we define a notion of bisimulation that allows to abstract a detailed probabilistic basic action theory with noisy actuators and sensors by a possibly non-stochastic basic action theory. By doing so, we obtain abstract Golog programs that omit unnecessary details and which can be translated back to a detailed program for actual execution. This simplifies the implementation of noisy robot programs, opens up the possibility of using non-stochastic reasoning methods (e.g., planning) on probabilistic problems, and provides domain descriptions that are more easily understandable and explainable.

翻译：抽象是一种常用方法，用于通过更粗略的规范来表示某些底层系统，其目的是在保留重要方面的同时省略不必要的细节。尽管近期关于情境演算中抽象的研究主要集中于非概率领域，我们提出了一种针对概率与动态系统的抽象方法。基于带有概率信念的情境演算变体，我们定义了一种双模拟概念，使得能够通过可能非随机的基动作理论来抽象具有噪声执行器和传感器的详细概率基动作理论。通过这种方式，我们获得了省略不必要细节的抽象Golog程序，这些程序可被转换回详细程序以进行实际执行。这简化了噪声机器人程序的实现，为在概率问题上使用非随机推理方法（如规划）开辟了可能性，并提供了更易理解和解释的领域描述。