Sequential decomposition of propositional logic programs
This work addresses a theoretical problem for researchers in logic programming and algebra, but it is incremental as it builds on recent introductions of sequential composition.
The paper tackles the problem of decomposing propositional logic programs sequentially by applying Green's relations from semigroup theory, resulting in a foundational step toward an algebraic theory of logic programming.
The sequential composition of propositional logic programs has been recently introduced. This paper studies the sequential {\em decomposition} of programs by studying Green's relations $\mathcal{L,R,J}$ -- well-known in semigroup theory -- between programs. In a broader sense, this paper is a further step towards an algebraic theory of logic programming.