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. First-order logic with imperfect information extends first-order logic by considering sentences whose semantic games have imperfect information.

Cylindric set algebras are to first-order logic as Boolean algebras are to propositional logic. In this talk, we will introduce a similar algebraization of first-order logic with imperfect information.