Recently I read all kinds of work from logic scientist in which epistemic logic was the main topic. Where epistmic change refers to change in knowledge of some agent in a multi-agent system (in a non-changing world), ontic change refers to change in the factual world.
What I was wondering about is how one can add the dimension of time to an epistemic system (or possibly in a system in which the ontic changes included). For example to formalize things like:
- After a certain point (in the future) A will know that $\varphi$ is the case (but up to then A does not know)
- A knows that after a certain point in the future, $\varphi$ will be the case (and she knows that until then, $\varphi$ is false.
- $B$ previously knew that $\psi$ was the case, but now (because, maybe the facts in the world changed) he does not know wheter $\psi$ is true.
where $A$, $B$, $\psi$, $\varphi$ are agents and propositional formulas
My main question is: what is the default paradigm/model/language/logical systems to express the sentences above? And how can one visualize it (for example by using (extended) Kripke-models?
Another question is how we can add the time dimension to dynamic epistemic logic ("after action $\alpha$ happened $A$ knows that there will be a time step in future (from) where $\tau$ is true" or anything like that).