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dependence logic
Dependence logic is a logical formalism, created by Jouko Väänänen,〔Väänänen 2007〕 which adds ''dependence atoms'' to the language of first-order logic. A dependence atom is an expression of the form , where are terms, and corresponds to the statement that the value of is functionally dependent on the values of .
Dependence logic is a logic of imperfect information, like branching quantifier logic or independence-friendly logic: in other words, its game theoretic semantics can be obtained from that of first-order logic by restricting the availability of information to the players, thus allowing for non-linearly ordered patterns of dependence and independence between variables. However, dependence logic differs from these logics in that it separates the notions of dependence and independence from the notion of quantification.
==Syntax==
The syntax of dependence logic is an extension of that of first-order logic. For a fixed signature σ = (''S''func, ''S''rel, ar), the set of all well-formed dependence logic formulas is defined according to the following rules:
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