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Logic, Probability and Action: A Situation Calculus Perspective
arXiv - CS - Symbolic Computation Pub Date : 2020-06-17 , DOI: arxiv-2006.09868
Vaishak Belle

The unification of logic and probability is a long-standing concern in AI, and more generally, in the philosophy of science. In essence, logic provides an easy way to specify properties that must hold in every possible world, and probability allows us to further quantify the weight and ratio of the worlds that must satisfy a property. To that end, numerous developments have been undertaken, culminating in proposals such as probabilistic relational models. While this progress has been notable, a general-purpose first-order knowledge representation language to reason about probabilities and dynamics, including in continuous settings, is still to emerge. In this paper, we survey recent results pertaining to the integration of logic, probability and actions in the situation calculus, which is arguably one of the oldest and most well-known formalisms. We then explore reduction theorems and programming interfaces for the language. These results are motivated in the context of cognitive robotics (as envisioned by Reiter and his colleagues) for the sake of concreteness. Overall, the advantage of proving results for such a general language is that it becomes possible to adapt them to any special-purpose fragment, including but not limited to popular probabilistic relational models.

中文翻译:

逻辑、概率和行动:情境演算的视角

逻辑和概率的统一是 AI 中的一个长期关注点,更广泛地说,是科学哲学中的一个问题。本质上,逻辑提供了一种简单的方法来指定必须在每个可能的世界中保持的属性,而概率允许我们进一步量化必须满足某个属性的世界的权重和比率。为此,已经进行了许多发展,最终提出了诸如概率关系模型之类的建议。虽然这一进展引人注目,但用于推理概率和动态(包括在连续设置中)的通用一阶知识表示语言仍有待出现。在本文中,我们调查了有关情景演算中逻辑、概率和动作的整合的最新结果,这可以说是最古老和最著名的形式主义之一。然后我们探索该语言的约简定理和编程接口。为了具体起见,这些结果是在认知机器人技术(如 Reiter 和他的同事所设想的)的背景下激发的。总体而言,为这种通用语言证明结果的优势在于,可以使它们适应任何特殊用途的片段,包括但不限于流行的概率关系模型。
更新日期:2020-06-18
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