  This paper contributes to the mathematical foundations of logic programming
by introducing and studying the sequential composition of answer set programs.
On the semantic side, we show that the immediate consequence operator of a
program can be represented via composition, which allows us to compute the
least model semantics of Horn programs without any explicit reference to
operators. As a result, we can characterize answer sets algebraically, which
further provides an algebraic characterization of strong and uniform
equivalence which is appealing. This bridges the conceptual gap between the
syntax and semantics of an answer set program in a mathematically satisfactory
way. The so-obtained algebraization of answer set programming allows us to
transfer algebraic concepts into the ASP-setting which we demonstrate by
introducing the index and period of an answer set program as an algebraic
measure of its cyclicality. The technical part of the paper ends with a brief
section introducing the algebraically inspired novel class of aperiodic answer
set programs strictly containing the acyclic ones. In a broader sense, this
paper is a first step towards an algebra of answer set programs and in the
future we plan to lift the methods of this paper to wider classes of programs,
most importantly to higher-order and disjunctive programs and extensions
thereof.
