An Ehrenfeucht-fraïssé Game for Inquisitive First-order Logic

Inquisitive first-order logic, InqBQ, extends classical first-order logic with questions. From a technical perspective, InqBQ allows us to talk about a plurality of first-order structures, expressing not only facts about each structure in isolation, but also about how these structures relate to each other. We describe an Ehrenfeucht-Fräıssé game for InqBQ and show that this characterizes the expressive power of the logic. We illustrate the usefulness of the result by giving a game-theoretic proof of the fact that certain cardinality properties are not expressible in InqBQ.