This paper gives a theory of inference to logically reason symbolic knowledge fully from data over time. We propose a temporal probabilistic model that generates symbolic knowledge from data. The statistical correctness of the model is justified in terms of consistency with Kolmogorov's axioms, Fenstad's theorems and maximum likelihood estimation. The logical correctness of the model is justified in terms of logical consequence relations on propositional logic and its extension. We show that the theory is applicable to localisation problems.

翻译：本文给出了一个逻辑推理理论, 逻辑推理上的象征性知识完全来自数据随时间推移。 我们提出了一个时间概率模型, 从数据中产生象征性知识。 模型的统计正确性从与科尔莫戈罗夫的正数、 Fenstad 的定理和最大可能性估算的一致性来看是有道理的。 模型逻辑正确性从理论逻辑及其延伸的逻辑后果关系来看是合理的。 我们显示,该理论适用于本地化问题。