In the middle of the nineteenth century two new fields - universal algebra and formal logic - came into being. They both originated in George Boole’s ideas. The quickest development and the most remarkable features of the reunion of algebra and logic took place in the 1930s due to discoveries of Birkhoff, Tarski and Lindenbaum. Nowadays, universal algebra is one of the most important tools used in logical investigations.

The aim of this tutorial is to present some important notions and theorems of universal algebra and their applications to formal logic.
In the first part we explain basic notions of universal algebra, like an algebraic structure, a set of generators, homomorphisms, products, congruences, varieties and free algebras.
In the second part we present the elements of lattice theory which are especially useful in description of algebras of different types of logics.

References

J.M.Dunn and G.M.Hardegree Algebric Methods in Philosophical Logic, Clarendon Press, Oxford, 2001.
G.Grätzer, Universal Algebra, Second Edition, Springer - Verlag, New York – Heidelberg – Berlin, 1979.
Lecture Notes