Recently I read all kinds of work from logic scientists 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 p is the case (but up to then A does not know that p, while it was already the case)
- A knows that after a certain point in the future, p will be the case (and she knows that until then, p is not the point.
- B previously knew that p was the case, but now (because, maybe the facts in the world changed or A had a brain attack) does not know wheter p is true.
where A,B,q 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?