I'm learning the basics of RL and I'm struggling to understand the notion of terminal state in MDPs.
To ask my question straightforwardly: is there a natural way to define the terminal state from the MDP transition probabilities $p(s',r|s,a)$? If I need to be more restrictive, assume a game setting, for example, chess.
My first hypothesis would be to define the terminal state as the state $s_T$ such that $p(s',r|s_T,a) = p(s',r|s_T)$, a state from which the transition is independent of the agent's actions. But that does not seem quite right. First, there is no particular reason why this state should be unique. Second, from this definition, it could also just be an intermittent state of "lag".