So I have been looking into Modal Logic as well as epistemic logic (and its dynamic versions) with the hopes of studying their applications to Fitch's paradox.
Fitches paradox refers to the proof that from the supposition that everything true is knowable, we get that everything true is already known, which seems absurd.
My main question is that this seems to specify a very particular language. So my understanding has been that:
Modal logic: Necessitation = Box (for all related worlds) Possibility = Diamond (there exists related world)
Epistemic Logic: Necessitation = K_a (for all related states), Possibility = K^ (there exists related state)
However most proofs of Fitch's paradox seems to model 'knowable' as (Diamond K p), which seems to combine both languages together. I find it difficult to interpret what this specific language means, and what Diamond here really refers to. For example, if I wanted to formally model the language that includes both K and Diamond, what would be the semantics?
Thanks so much