 The logical matrix models of a given logic can be thought of as algebraic generalizations of its theories, more precisely, of its Lindenbaum matrices. They come from taking a local perspective centered around the theories of the logic considered one by one and its analogs the logic filters (also taken one by one). But, as we will see, the properties of a logic depend in general on the global behavior of the set of its theories taken together as a bunch; or —to put it otherwise— on its consequence relation. The consideration of this global behavior introduces a global perspective on the design of semantics for logic systems. The abstract logics that we are going to define can be seen, in contrast to logical matrices, as algebraic generalizations of the logic itself and its extensions. They are the natural objects to consider when one takes the global perspective seriously.