COMPLETE LOGICS FOR ELEMENTARY TEAM PROPERTIES

Abstract

Abstract In this paper, we introduce a logic based on team semantics, called $\mathbf {FOT} $ , whose expressive power is elementary, i.e., coincides with first-order logic both on the level of sentences and (possibly open) formulas, and we also show that a sublogic of $\mathbf {FOT} $ , called $\mathbf {FOT}^{\downarrow } $ , captures exactly downward closed elementary (or first-order) team properties. We axiomatize completely the logic $\mathbf {FOT} $ , and also extend the known partial axiomatization of dependence logic to dependence logic enriched with the logical constants in $\mathbf {FOT}^{\downarrow } $ .