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Team Logic and Second-Order Logic

Kontinen J., Nurmi V.

Fundamenta Informaticae

2011

Vol. 106, nr 2-4

259-272

Team logic is a new logic, introduced by V¨a¨an¨anen [12], extending dependence logic by classical negation. Dependence logic adds to first-order logic atomic formulas expressing functional dependence of variables on each other. It is known that on the level of sentences dependence logic and team logic are equivalent with existential second-order logic and full second-order logic, respectively. In this article we show that, in a sense that we make explicit, team logic and secondorder logic are also equivalent with respect to open formulas. A similar earlier result relating open formulas of dependence logic to the negative fragment of existential second-order logic was proved in [8].