On Sahlqvist theory for hybrid logics

We develop a Sahlqvist theory by introducing the class of hybrid inductive formulas. Each hybrid inductive formula is shown to have an effectively calculable first-order local frame correspondent. We define two subclasses, called the nominally skeletal and skeletal hybrid inductive formulas. We show that members of these subclasses are, respectively, preserved under canonical extensions and Dedekind–MacNeille completions of certain hybrid algebras, which is enough to ensure that these formulas axiomatize relationally complete logics. The key methodological tool in proving these results is a hybrid version of the ALBA algorithm, which we formulate and call hybrid-ALBA.