Epistemic Operators in Dependence Logic

Abstract

The properties of the $${\forall^{1}}$$ quantifier defined by Kontinen and Vaananen in [13] are studied, and its definition is generalized to that of a family of quantifiers $${\forall^{n}}$$ . Furthermore, some epistemic operators ? n for Dependence Logic are also introduced, and the relationship between these $${\forall^{n}}$$ quantifiers and the ? n operators are investigated. The Game Theoretic Semantics for Dependence Logic and the corresponding Ehrenfeucht- Fraisse game are then adapted to these new connectives. Finally, it is proved that the $${\forall^{1}}$$ quantifier is not uniformly definable in Dependence Logic, thus answering a question posed by Kontinen and Vaananen in the above mentioned paper.