Sequential composition of propositional logic programs

TL;DR

This paper explores the sequential composition and decomposition of propositional logic programs, offering new methods to analyze their structure and compute models more efficiently by linking syntax and semantics.

Contribution

It introduces the concept of sequential composition and decomposition for propositional logic programs, providing a novel way to analyze and compute their least models.

Findings

Acyclic programs can be decomposed into single-rule programs.

The immediate consequence operator can be represented via composition.

Least models can be computed without explicit operators.

Abstract

This paper introduces and studies the sequential composition and decomposition of propositional logic programs. We show that acyclic programs can be decomposed into single-rule programs and provide a general decomposition result for arbitrary programs. We show that the immediate consequence operator of a program can be represented via composition which allows us to compute its least model without any explicit reference to operators. This bridges the conceptual gap between the syntax and semantics of a propositional logic program in a mathematically satisfactory way.