the introduction of if logic was partly motivated by the attempt of extending the game semantics of first-order logic to games of imperfect information. indeed, a semantics for if sentences can be given in terms of these kinds of games (or, alternatively, by means of a translation procedure to existential second-order logic). a semantics for open formulas cannot be given in the form of a tarskian semantics (); an adequate semantics must specify what it means for a formula to be satisfied by a set of assignments of common variable domain (a "team") rather than satisfaction by a single assignment. such a "team semantics" was developed by hodges ().