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Generalized Quantifiers in Dependence Logic

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Abstract

We introduce generalized quantifiers, as defined in Tarskian semantics by Mostowski and Lindström, 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 independence atom recently introduced by Väänänen and Grädel.

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Correspondence to Fredrik Engström.

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Engström, F. Generalized Quantifiers in Dependence Logic. J of Log Lang and Inf 21, 299–324 (2012). https://doi.org/10.1007/s10849-012-9162-4

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Keywords

  • Dependence logic
  • Independence friendly logic
  • Generalized quantifiers
  • Multi valued dependence