Quasi-varieties and initial semantics for hybridized institutions

We define and develop the concept of quasi-variety for models of hybrid logics and we apply this for determining initial semantics for classes of hybrid logics theories. The hybrid logic is considered here in a very general sense, internal to abstract institutions (in the sense of the so-called institution theory of Goguen and Burstall). This means our result is applicable to a wide variety of hybrid logics including for example those resulting from the various kinds of combinations between conventional hybrid logics and various other logical systems.