Abstract Reasoning about degrees of belief in uncertain dynamic worlds is fundamental to many applications, such as robotics and planning, where actions modify state properties and sensors provide measurements, both of which are prone to noise. With the exception of limited cases such as Gaussian processes over linear phenomena, belief state evolution can be complex and hard to reason with in a general way, especially when the agent has to deal with categorical assertions, incomplete information such as disjunctive knowledge, as well as probabilistic knowledge. Among the many approaches for reasoning about degrees of belief in the presence of noisy sensing and acting, the logical account proposed by Bacchus, Halpern, and Levesque is perhaps the most expressive, allowing for such belief states to be expressed naturally as constraints. While that proposal is powerful, the task of how to plan effectively is not addressed. In fact, at a more fundamental level, the task of projection, that of reasoning about beliefs effectively after acting and sensing, is left entirely open. To aid planning algorithms, we study the projection problem in this work. In the reasoning about actions literature, there are two main solutions to projection: regression and progression. Both of these have proven enormously useful for the design of logical agents, essentially paving the way for cognitive robotics. Roughly, regression reduces a query about the future to a query about the initial state. Progression, on the other hand, changes the initial state according to the effects of each action and then checks whether the formula holds in the updated state. In this work, we show how both of these generalize in the presence of degrees of belief, noisy acting and sensing. Our results allow for both discrete and continuous probability distributions to be used in the specification of beliefs and dynamics.

中文翻译：

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随机域中的回归和进展

摘要 对不确定动态世界的置信度进行推理是许多应用的基础，例如机器人和规划，其中动作修改状态属性，传感器提供测量，两者都容易产生噪声。除了线性现象上的高斯过程等有限情况外，信念状态演化可能很复杂且难以以一般方式进行推理，尤其是当智能体必须处理分类断言、不完整信息（如析取知识）以及作为概率知识。在存在噪声感知和行动的情况下对信念程度进行推理的众多方法中，巴克斯、哈尔彭和莱维斯克提出的逻辑解释可能是最具表现力的，允许将这种信念状态自然地表达为约束。尽管该提议很有力，但没有解决如何有效规划的任务。事实上，在更基本的层面上，投射的任务，即在行动和感知之后有效地推理信念的任务，是完全开放的。为了帮助规划算法，我们研究了这项工作中的投影问题。在关于行动的推理文献中，有两种主要的投影解决方案：回归和进展。事实证明，这两者对于逻辑代理的设计非常有用，基本上为认知机器人铺平了道路。粗略地说，回归将关于未来的查询简化为关于初始状态的查询。另一方面，Progression 根据每个动作的效果改变初始状态，然后检查公式是否在更新状态下成立。在这项工作中，我们展示了这两者如何在存在程度的信念、嘈杂的行为和感知的情况下概括。我们的结果允许将离散和连续概率分布用于信念和动态的规范。