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.
12.
This also has the same ? sentences as EFA, in the sense that whenever EFA proves " x " y P ( x, y ), with P quantifier-free, ERA proves the open formula P ( x, T ( x ) ), with T a term definable in ERA.
13.
As for open formulas, dependence logic corresponds to the downwards monotone fragment of existential second-order logic, in the sense that a nonempty class of teams is definable by a dependence logic formula if and only if the corresponding class of relations is downwards monotone and definable by an existential second-order formula.
14.
IF logic is translation equivalent, at the level of sentences, with a number of other logical systems based on team semantics, such as dependence logic, dependence-friendly logic, exclusion logic and independence logic; with the exception of the latter, IF logic is known to be equiexpressive to these logics also at the level of open formulas.
15.
A universal quantification of an open formula & phi; is true in a model iff every element in the domain satisfies that formula . ( Note that in the metalanguage, " everything that is such that X is such that Y " is interpreted as a universal generalization of the material conditional " if anything is such that X then it is such that Y ".
