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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)

We study definability in terms of monotone generalized quantifiers satisfying Isomorphism closure, Conservativity and Extension. Among the quantifiers with the latter three properties — here called CE quan-tifiers — one finds the interpretations of determiner phrases in natural languages. The property of monotonicity is also linguistically ubiquitous ,… (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)