### Abstract

The theorem on loop formulas due to Fangzhen Lin and Yuting Zhao shows how to turn a logic program into a propositional formula that describes the program's stable models. In this paper we simplify and generalize the statement of this theorem. The simplification is achieved by modifying the definition of a loop in such a way that a program is turned into the corresponding propositional formula by adding loop formulas directly to the conjunction of its rules, without the intermediate step of forming the program's completion. The generalization makes the idea of a loop formula applicable to stable models in the sense of a very general definition that covers disjunctive programs, programs with nested expressions, and more.

Original language | English (US) |
---|---|

Pages (from-to) | 79-101 |

Number of pages | 23 |

Journal | Annals of Mathematics and Artificial Intelligence |

Volume | 47 |

Issue number | 1-2 |

DOIs | |

State | Published - Jun 2006 |

### Fingerprint

### Keywords

- Answer set programming
- Clark's completion
- Logic programming
- Loop formulas
- Nonmonotonic reasoning
- Stable models

### ASJC Scopus subject areas

- Artificial Intelligence
- Applied Mathematics

### Cite this

*Annals of Mathematics and Artificial Intelligence*,

*47*(1-2), 79-101. https://doi.org/10.1007/s10472-006-9025-2

**A generalization of the Lin-Zhao theorem.** / Ferraris, Paolo; Lee, Joohyung; Lifschitz, Vladimir.

Research output: Contribution to journal › Article

*Annals of Mathematics and Artificial Intelligence*, vol. 47, no. 1-2, pp. 79-101. https://doi.org/10.1007/s10472-006-9025-2

}

TY - JOUR

T1 - A generalization of the Lin-Zhao theorem

AU - Ferraris, Paolo

AU - Lee, Joohyung

AU - Lifschitz, Vladimir

PY - 2006/6

Y1 - 2006/6

N2 - The theorem on loop formulas due to Fangzhen Lin and Yuting Zhao shows how to turn a logic program into a propositional formula that describes the program's stable models. In this paper we simplify and generalize the statement of this theorem. The simplification is achieved by modifying the definition of a loop in such a way that a program is turned into the corresponding propositional formula by adding loop formulas directly to the conjunction of its rules, without the intermediate step of forming the program's completion. The generalization makes the idea of a loop formula applicable to stable models in the sense of a very general definition that covers disjunctive programs, programs with nested expressions, and more.

AB - The theorem on loop formulas due to Fangzhen Lin and Yuting Zhao shows how to turn a logic program into a propositional formula that describes the program's stable models. In this paper we simplify and generalize the statement of this theorem. The simplification is achieved by modifying the definition of a loop in such a way that a program is turned into the corresponding propositional formula by adding loop formulas directly to the conjunction of its rules, without the intermediate step of forming the program's completion. The generalization makes the idea of a loop formula applicable to stable models in the sense of a very general definition that covers disjunctive programs, programs with nested expressions, and more.

KW - Answer set programming

KW - Clark's completion

KW - Logic programming

KW - Loop formulas

KW - Nonmonotonic reasoning

KW - Stable models

UR - http://www.scopus.com/inward/record.url?scp=33750972879&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33750972879&partnerID=8YFLogxK

U2 - 10.1007/s10472-006-9025-2

DO - 10.1007/s10472-006-9025-2

M3 - Article

VL - 47

SP - 79

EP - 101

JO - Annals of Mathematics and Artificial Intelligence

JF - Annals of Mathematics and Artificial Intelligence

SN - 1012-2443

IS - 1-2

ER -