  The primary goal of this paper is to present a unified way to transform the
syntax of a logic system into certain initial algebraic structure so that it
can be studied algebraically. The algebraic structures which one may choose for
this purpose are various clones over a full subcategory of a category. We show
that the syntax of equational logic, lambda calculus and first order logic can
be represented as clones or right algebras of clones over the set of positive
integers. The semantics is then represented by structures derived from left
algebras of these clones.
