# Dependence logic and generalized quantifiers

## Fredrik Engström, FLoV

Dependence logic, proposed by Väänänen, is an elegant way of introducing dependencies between variables into the object language. The framework of Dependence logic, so-called team semantics, has turned out to be very flexible and allows for interesting generalizations. Instead of considering satisfaction with respect to a single assignment s, team semantics considers sets of assignments X, called teams. While the semantics of Dependence logic is based on the principle that a formula φ is satisfied by a team X if every assignment s ∈ X satisfies φ, we will replace this principle by the following: a formula φ is satisfied by a team X if for every assignment s: s ∈ X iff s satisfies φ, replacing an implication by an equivalence. When only first-order logic is considered nothing exciting happens, it is only when we introduce new logical operations that things start to get more exciting.