Module Theorem for The General Theory of Stable Models
This work provides a theoretical extension for researchers in answer set programming, allowing more flexible program analysis and incremental computation, but it is incremental as it builds on existing theorems.
The authors extended the module theorem from answer set programming to the general theory of stable models, enabling modular structures for non-ground logic programs with constructs like choice rules and aggregates, and reformulated incremental answer set computation for a broader class of programs.
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.