In human-robot interaction policy design, a rule-based method is efficient, explainable, expressive and intuitive. In this paper, we present the Signal-Rule-Slot framework, which refines prior work on rule-based symbol system design and introduces a new, Bayesian notion of interaction rule utility called Causal Pathway Self-information. We offer a rigorous theoretical foundation as well as a rich open-source reference implementation Ravestate, with which we conduct user studies in text-, speech-, and vision-based scenarios. The experiments show robust contextual behaviour of our probabilistically informed rule-based system, paving the way for more effective human-machine interaction.