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...rt of relationship with other notions of dependency. We will later recall the full definition of the team semantics of dependence logic, an adaptation of Hodges’ compositional semantics for IF-logic (=-=[21]-=-) and one of the three equivalent semantics for dependence logic described in [32].5 It is worth noting already here, though, that the key difference between Hodges semantics and the usual Tarskian se...

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... is the Boolean closure of IF , that is, the closure of IF under the operations (1) ; (5) :: 1 Hintikka and Sandu define the semantics of IF via a non-determined game of imperfect information. Hodges =-=[5]-=- gives an equivalent inductive truth definition a'la Tarski, which actually makes the semantics compositional. Caicedo and Krynicki [1] use a variation of Hodges' truth-definition and prove a Prenex N...

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...oise chooses for v, she does not know what Abelard chose for x. To make this explicit, the logic is written with a more general syntax which is linear rather than two dimensional. We here use Hodges' =-=[Hod97]-=- syntax, which addresses certain flaws in Hintikka's; and for reasons of space and simplicity, we omit some operators in this version. IF-FOL + is obtained from FOL + by modifying the syntax of quanti...

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...ication whether the variables y and z are going to be universally or existentially quantified; so from the formula alone we don’t know what information can be fed into the Skolem functions for it. In =-=[5]-=- I sidestepped this second problem by replacing the Skolem functions by general game strategies. Unlike a Skolem function, a strategy for a player can call on previous choices of either player. For ga...

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...here are many different intuitive meanings for =(⃗y, ⃗x), such as “⃗y totally determines ⃗x” or “⃗x is a function of ⃗y”, the best way to understand the concept is to give it semantics: Definition 1 (=-=[3, 5]-=-). Sets of assigments are called teams. A team X satisfies =(⃗y, ⃗x) in M, in symbols M |=X =(⃗y, ⃗x), or just X |= =(⃗y, ⃗x), if ∀s, s ′ ∈ X(s(⃗y) = s ′ (⃗y) → s(⃗x) = s ′ (⃗x)). (1) Condition (1) is...

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...c [14, 22], and its study has sparked the development of a whole family of logics obtained by adding various dependency conditions into First Order Logic. All these logics are based on Team Semantics =-=[16, 24]-=- which is a generalization of Tarski Semantics. In Team Semantics, formulas are satisfied or not satisfied by sets of assignments, called teams, rather than by single assignments. This semantics was i...

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...ct given in [29]. It should be noted that we use the term “IF logic” in a generic sense, making no terminological distinction between Hintikka and Sandu’s [4] original version of IF logic and Hodge’s =-=[5]-=- generalization of it termed in [6] slash logic. In fact, both the syntax and the semantics for IF formulas that we use are those of slash logic. It is assumed that all formulas of IF logic are writte...

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...he IF-logic of Hintikka and Sandu [HS89, HS95, HS96]. The issue of whether and how a compositional semantics for IF-logic can be given has been studied by several authors, particularly Wilfrid Hodges =-=[Hod97]-=-. However, there is an even more basic question which does not seem to have received much, if any, attention: namely, how to give a properly compositional syntax for such constructs. For example, how ...