This paper gives a simple theory of inference to logically reason symbolic knowledge fully from data over time. We take a Bayesian approach to model how data causes symbolic knowledge. Probabilistic reasoning with symbolic knowledge is modelled as a process of going the causality forwards and backwards. The forward and backward processes correspond to an interpretation and inverse interpretation of formal logic, respectively. The theory is applied to a localisation problem to show a robot with broken or noisy sensors can efficiently solve the problem in a fully data-driven fashion.

翻译：本文提出一种简单的推理理论，用于基于时序数据完全逻辑地推理符号知识。我们采用贝叶斯方法建模数据如何引发符号知识。将符号知识的概率推理建模为因果关系的前向与反向过程，其中前向与反向过程分别对应形式逻辑的解释与逆解释。该理论被应用于定位问题，以展示配备破损或噪声传感器的机器人能够以完全数据驱动的方式高效解决该问题。