Abstract algebraic logic has become a well established subfield of algebraic logic, with many deep and interesting results. These results explain many properties of different classes of logical systems previously explained only on a case-by-case basis or shrouded in mystery. Perhaps the most important achievement of abstract algebraic logic has been the classification of propositional logics in a hierarchy, called the abstract algebraic hierarchy or Leibniz hierarchy, whose different levels roughly reflect the strength of the ties between a logic at a particular level and its associated class of algebras. The position of a logic in this hierarchy determines the extent to which that logic may be studied using known algebraic methods and techniques. Once a logic is assigned to a level of this hierarchy, one may draw on the powerful arsenal of results, accumulated over the past 30-odd years, governing the algebras situated at the same level of the hierarchy.
