  The concept of a clone is central to many branches of mathematics, such as
universal algebra, algebraic logic, and lambda calculus. Abstractly a clone is
a category with two objects such that one is a countably infinite power of the
other. Left and right algebras over a clone are covariant and contravariant
functors from the category to that of sets respectively. In this paper we show
that first-order logic can be studied effectively using the notions of right
and left algebras over a clone. It is easy to translate the classical treatment
of logic into our setting and prove all the fundamental theorems of first-order
theory algebraically.
