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.