A Gentle Introduction to Abstract Algebraic Logic

Algebraic logic is the branch of mathematical logic that
studies logical systems by giving them algebraic semantics.
It mainly capitalizes on the standard Linbenbaum-Tarski
proof of completeness of classical logic w.r.t. the
two-element Boolean algebra, which can be analogously
repeated in other logical systems yielding completeness
w.r.t. other kinds of algebras. Abstract algebraic logic
(AAL) determines what are the essential elements in these
proofs and develops an abstract theory of the possible ways
in which logical systems can be related to an algebraic
counterpart. The usefulness of these methods is witnessed
by the fact that the study of many logics, relevant for
mathematics, computer science, linguistics or philosophical
purposes, has greatly benefited from the algebraic
approach, that allows to understand their properties in
terms of equivalent algebraic properties of their semantics.

This course is a self-contained introduction to AAL. We
start from the very basics of AAL, develop its general and
systematic theory and illustrate the results with
applications to particular examples of propositional logics.