Learning in a changing world via algebraic modal logic

We develop an algebraic modal logic that combines epistemic modalities with dynamic modalities with a view to modelling information acquisition (learning) by automated agents in a changing world. Unlike most treatments of dynamic epistemic logic, we have transitions that “change the state” of the underlying system and not just the state of knowledge of the agents. The key novel feature that emerges is the need to have a way of “inverting transitions” and distinguishing between transitions that “really happen” and transitions that are possible. Our approach is algebraic, rather than being based on a Kripke-style semantics. The semantics are given in terms of quantales. We study a class of quantales with the appropriate inverse operations and prove soundness and completeness theorems. We illustrate the ideas with a simple game as well as a toy robot-navigation problem. The examples illustrate how an agent discovers information by taking actions.