A Double Team Semantics for Generalized Quantifiers

We investigate extensions of dependence logic with generalized quantifiers. We also introduce and investigate the notion of a generalized atom. We define a system of semantics that can accommodate variants of dependence logic, possibly extended with generalized quantifiers and generalized atoms, under the same umbrella framework. The semantics is based on pairs of teams, or double teams. We also devise a game-theoretic semantics equivalent to the double team semantics. We make use of the double team semantics by defining a logic [Formula: see text] which canonically fuses together two-variable dependence logic[Formula: see text] and two-variable logic with counting quantifiers[Formula: see text]. We establish that the satisfiability and finite satisfiability problems of [Formula: see text] are complete for [Formula: see text].