Boolean Dependence Logic and Partially-Ordered Connectives

Abstract

We introduce a new variant of dependence logic (D) called Boolean dependence logic (BD). In BD dependence atoms are of the type =(x 1 , . . . , x n , α), where α is a Boolean variable. Intuitively, with Boolean dependence atoms one can express quantification of relations, while standard dependence atoms express quantification over functions.We compare the expressive power of BD to D and first-order logic enriched by partially-ordered connectives, F O(POC). We show that the expressive power of BD and D coincide. We define natural syntactic fragments of BD and show that they coincide with the corresponding fragments of F O(POC) with respect to expressive power. We then show that the fragments form a strict hierarchy.