Actions, Continuous Distributions and Meta-Beliefs

In this work, we propose a new modal logical language for reasoning about noisy actions and sensors in an epistemic setting. In the reasoning about actions literature, there are only a few frameworks for modelling probabilistic noise, and even less in dealing with continuous probability distributions. In the first model of its kind, we show how a rich theory of actions with beliefs, meta-beliefs and only knowing can be defined over discrete, continuous and mixed discrete-continuous distributions.