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We introduce an atomic formula y ⊥ x z intuitively saying that the variables y are independent from the variables z if the variables x are kept constant. We contrast this with dependence logic D based on the atomic formula =(x, y), actually equivalent to y ⊥ x y, saying that the variables y are totally determined by the variables x. We show that y ⊥ x z… (More)

We study the expressive power of open formulas of dependence logic introduced in Väänänen [Dependence logic (Vol. 70 of London Mathematical Society Student Texts), 2007]. In particular, we answer a question raised by Wilfrid Hodges: how to characterize the sets of teams definable by means of identity only in dependence logic, or equivalently in independence… (More)

The semantics of the independence friendly logic of Hintikka and Sandu is usually deened via a game of imperfect information. We give a new deenition in terms of a game of perfect information. We also give an Ehrenfeucht-Fra ss e game adequate for this logic. We consider a logic IF which is the closure of atomic and negated atomic formulas of rst order… (More)

The concept of a generalized quantiier of a given similarity type was deened in Lin66]. Our main result says that on nite structures diierent similarity types give rise to diierent classes of generalized quantiiers. More exactly, for every similarity type t there is a generalized quantiier of type t which is not deenable in the extension of rst order logic… (More)