Generalizing Modular Logic Programs

TL;DR

This paper extends the modularity framework for Answer Set Programming by relaxing restrictive conditions, thereby broadening its applicability and enhancing the theoretical foundation of module composition.

Contribution

It introduces alternative methods to lift restrictions on module conditions, expanding the scope of the existing module theorem in ASP.

Findings

Broadened the applicability of the module theorem in ASP

Proposed alternative approaches to module restrictions

Enhanced theoretical understanding of module composition in ASP

Abstract

Even though modularity has been studied extensively in conventional logic programming, there are few approaches on how to incorporate modularity into Answer Set Programming, a prominent rule-based declarative programming paradigm. A major approach is Oikarinnen and Janhunen's Gaifman-Shapiro-style architecture of program modules, which provides the composition of program modules. Their module theorem properly strengthens Lifschitz and Turner's splitting set theorem for normal logic programs. However, this approach is limited by module conditions that are imposed in order to ensure the compatibility of their module system with the stable model semantics, namely forcing output signatures of composing modules to be disjoint and disallowing positive cyclic dependencies between different modules. These conditions turn out to be too restrictive in practice and in this paper we discuss alternative ways of lift both restrictions independently, effectively solving the first, widening the applicability of this framework and the scope of the module theorem.