Generalized quantifiers in Dependence Logic

Details Generalized quantifiers in Dependence Logic Generalized quantifiers in Dependence Logic

2011-03-02

arxiv.org/abs/1103.0396v4

Mathematics

Logic

22 pages

Scientific paper

10.1007/s10849-012-9162-4

We introduce generalized quantifiers, as defined in Tarskian semantics by Mostowski and Lindstr\"om, in logics whose semantics is based on teams instead of assignments, e.g., IF-logic and Dependence logic. Both the monotone and the non-monotone case is considered. It is argued that to handle quantifier scope dependencies of generalized quantifiers in a satisfying way the dependence atom in Dependence logic is not well suited and that the multivalued dependence atom is a better choice. This atom is in fact definably equivalent to the \emph{independence atom} recently introduced by V\"a\"an\"anen and Gr\"adel.

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