Stream Reasoning Using Temporal Logic and Predictive Probabilistic State Models

Integrating logical and probabilistic reasoning and integrating reasoning over observations and predictions are two important challenges in AI. In this paper we propose P-MTL as an extension to Metric Temporal Logic supporting temporal logical reasoning over probabilistic and predicted states. The contributions are (1) reasoning over uncertain states at single time points, (2) reasoning over uncertain states between time points, (3) reasoning over uncertain predictions of future and past states and (4) a computational environment formalism that ground the uncertainty in observations of the physical world. Concrete robot soccer examples are given.