### Abstract

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.

Original language | English (US) |
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Pages (from-to) | 719-735 |

Number of pages | 17 |

Journal | Theory and Practice of Logic Programming |

Volume | 12 |

Issue number | 4-5 |

DOIs | |

State | Published - Jul 1 2012 |

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### Keywords

- answer set programming
- module theorem
- splitting theorem

### ASJC Scopus subject areas

- Software
- Theoretical Computer Science
- Hardware and Architecture
- Computational Theory and Mathematics
- Artificial Intelligence

### Cite this

*Theory and Practice of Logic Programming*,

*12*(4-5), 719-735. https://doi.org/10.1017/S1471068412000269