Generative Logic with Time: Beyond Logical Consistency and Statistical Possibility

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.