Module Theorem for The General Theory of Stable Models

TL;DR

This paper extends the module theorem to the general theory of stable models, enabling modular analysis and incremental computation for more complex answer set programs with advanced constructs.

Contribution

It generalizes the module theorem to non-ground programs with constructs like choice rules and aggregates, linking it to the symmetric splitting theorem.

Findings

Extended module theorem to non-ground programs

Reformulated incremental answer set computation

Enabled modular analysis of complex ASP constructs

Abstract

The module theorem by Janhunen et al. demonstrates how to provide a modular structure in answer set programming, where each module has a well-defined input/output interface which can be used to establish the compositionality of answer sets. The theorem is useful in the analysis of answer set programs, and is a basis of incremental grounding and reactive answer set programming. We extend the module theorem to the general theory of stable models by Ferraris et al. The generalization applies to non-ground logic programs allowing useful constructs in answer set programming, such as choice rules, the count aggregate, and nested expressions. Our extension is based on relating the module theorem to the symmetric splitting theorem by Ferraris et al. Based on this result, we reformulate and extend the theory of incremental answer set computation to a more general class of programs.