In the semantic game for a first-order sentence, one player (Eloise) attempts to verify the sentence by choosing the values of existentially quantified variables, while her opponent (Abelard) tries to falsify the sentence by picking the values of universally quantified variables. Disjunctions prompt the verifier to choose a disjunct; conjunctions prompt the falsifier to pick a conjunct. Negations tell the players to switch roles.

Stochastic first-order logic with imperfect information extends first-order logic by considering sentences whose semantic games have imperfect information and chance moves. In this talk, we will show how stochastic first-order logic can be used to analyze famous problems such as Monty Hall and Sleeping Beauty.