### Abstract

Answer Set Programming (ASP) is logic programming under the stable model or answer set semantics. During the last decade, this paradigm has seen several extensions by generalizing the notion of atom used in these programs. Among these, there are dl-atoms, aggregate atoms, HEX atoms, generalized quantifiers, and abstract constraints. In this paper we refer to these constructs collectively as generalized atoms. The idea common to all of these constructs is that their satisfaction depends on the truth values of a set of (non-generalized) atoms, rather than the truth value of a single (non-generalized) atom. Motivated by several examples, we argue that for some of the more intricate generalized atoms, the previously suggested semantics provide unintuitive results and provide an alternative semantics, which we call supportedly stable or SFLP answer sets. We show that it is equivalent to the major previously proposed semantics for programs with convex generalized atoms, and that it in general admits more intended models than other semantics in the presence of non-convex generalized atoms. We show that the complexity of supportedly stable answer sets is on the second level of the polynomial hierarchy, similar to previous proposals and to answer sets of disjunctive logic programs.

Original language | English |
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Title of host publication | Web Reasoning and Rule Systems - 9th International Conference, RR 2015, Proceedings |

Publisher | Springer Verlag |

Pages | 30-44 |

Number of pages | 15 |

Volume | 9209 |

ISBN (Print) | 9783319220017 |

DOIs | |

Publication status | Published - 2015 |

Event | 9th International Conference on Web Reasoning and Rule Systems - Berlin, Germany Duration: 4 Aug 2015 → 5 Aug 2015 Conference number: 9 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 9209 |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Conference

Conference | 9th International Conference on Web Reasoning and Rule Systems |
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Abbreviated title | RR 2015 |

Country | Germany |

City | Berlin |

Period | 4/08/15 → 5/08/15 |

### Fingerprint

### Cite this

*Web Reasoning and Rule Systems - 9th International Conference, RR 2015, Proceedings*(Vol. 9209, pp. 30-44). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9209). Springer Verlag. https://doi.org/10.1007/978-3-319-22002-4_4

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*Web Reasoning and Rule Systems - 9th International Conference, RR 2015, Proceedings.*vol. 9209, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9209, Springer Verlag, pp. 30-44, 9th International Conference on Web Reasoning and Rule Systems, Berlin, Germany, 4/08/15. https://doi.org/10.1007/978-3-319-22002-4_4

**Supportedly stable answer sets for logic programs with generalized atoms.** / Alviano, Mario; Faber, Wolfgang.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Supportedly stable answer sets for logic programs with generalized atoms

AU - Alviano, Mario

AU - Faber, Wolfgang

PY - 2015

Y1 - 2015

N2 - Answer Set Programming (ASP) is logic programming under the stable model or answer set semantics. During the last decade, this paradigm has seen several extensions by generalizing the notion of atom used in these programs. Among these, there are dl-atoms, aggregate atoms, HEX atoms, generalized quantifiers, and abstract constraints. In this paper we refer to these constructs collectively as generalized atoms. The idea common to all of these constructs is that their satisfaction depends on the truth values of a set of (non-generalized) atoms, rather than the truth value of a single (non-generalized) atom. Motivated by several examples, we argue that for some of the more intricate generalized atoms, the previously suggested semantics provide unintuitive results and provide an alternative semantics, which we call supportedly stable or SFLP answer sets. We show that it is equivalent to the major previously proposed semantics for programs with convex generalized atoms, and that it in general admits more intended models than other semantics in the presence of non-convex generalized atoms. We show that the complexity of supportedly stable answer sets is on the second level of the polynomial hierarchy, similar to previous proposals and to answer sets of disjunctive logic programs.

AB - Answer Set Programming (ASP) is logic programming under the stable model or answer set semantics. During the last decade, this paradigm has seen several extensions by generalizing the notion of atom used in these programs. Among these, there are dl-atoms, aggregate atoms, HEX atoms, generalized quantifiers, and abstract constraints. In this paper we refer to these constructs collectively as generalized atoms. The idea common to all of these constructs is that their satisfaction depends on the truth values of a set of (non-generalized) atoms, rather than the truth value of a single (non-generalized) atom. Motivated by several examples, we argue that for some of the more intricate generalized atoms, the previously suggested semantics provide unintuitive results and provide an alternative semantics, which we call supportedly stable or SFLP answer sets. We show that it is equivalent to the major previously proposed semantics for programs with convex generalized atoms, and that it in general admits more intended models than other semantics in the presence of non-convex generalized atoms. We show that the complexity of supportedly stable answer sets is on the second level of the polynomial hierarchy, similar to previous proposals and to answer sets of disjunctive logic programs.

UR - http://www.scopus.com/inward/record.url?scp=84951155712&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-22002-4_4

DO - 10.1007/978-3-319-22002-4_4

M3 - Conference contribution

AN - SCOPUS:84951155712

SN - 9783319220017

VL - 9209

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 30

EP - 44

BT - Web Reasoning and Rule Systems - 9th International Conference, RR 2015, Proceedings

PB - Springer Verlag

ER -