  Hintikka and Sandu's independence-friendly (IF) logic is a conservative
extension of first-order logic that allows one to consider semantic games with
imperfect information. In the present article, we first show how several
variants of the Monty Hall problem can be modeled as semantic games for IF
sentences. In the process, we extend IF logic to include semantic games with
chance moves and dub this extension stochastic IF logic. Finally, we use
stochastic IF logic to analyze the Sleeping Beauty problem, leading to the
conclusion that the thirders are correct while identifying the main error in
the halfers' argument.
