### Abstract

Defeasible reasoning is a simple but efficient approach to nonmonotonic reasoning that has recently attracted considerable interest and that has found various applications. Defeasible logic and its variants are an important family of defeasible reasoning methods. So far no relationship has been established between defeasible logic and mainstream nonmonotonic reasoning approaches. In this paper we establish close links to known semantics of logic programs. In particular, we give a translation of a defeasible theory D into a meta-program P(D). We show that under a condition of decisiveness, the defeasible consequences of D correspond exactly to the sceptical conclusions of P(D) under the stable model semantics. Without decisiveness, the result holds only in one direction (all defeasible consequences of D are included in all stable models of P(D)). If we wish a complete embedding for the general case, we need to use the Kunen semantics of P(D), instead.

Original language | English |
---|---|

Pages (from-to) | 703-735 |

Number of pages | 33 |

Journal | Theory and Practice of Logic Programming |

Volume | 6 |

Issue number | 6 |

Early online date | 16 Oct 2006 |

DOIs | |

Publication status | Published - 1 Nov 2006 |

Externally published | Yes |

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### Cite this

*Theory and Practice of Logic Programming*,

*6*(6), 703-735. https://doi.org/10.1017/S1471068406002778

}

*Theory and Practice of Logic Programming*, vol. 6, no. 6, pp. 703-735. https://doi.org/10.1017/S1471068406002778

**Embedding defeasible logic into logic programming.** / Antoniou, Grigoris; Billington, David; Governatori, Guido; Maher, Michael J.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Embedding defeasible logic into logic programming

AU - Antoniou, Grigoris

AU - Billington, David

AU - Governatori, Guido

AU - Maher, Michael J.

PY - 2006/11/1

Y1 - 2006/11/1

N2 - Defeasible reasoning is a simple but efficient approach to nonmonotonic reasoning that has recently attracted considerable interest and that has found various applications. Defeasible logic and its variants are an important family of defeasible reasoning methods. So far no relationship has been established between defeasible logic and mainstream nonmonotonic reasoning approaches. In this paper we establish close links to known semantics of logic programs. In particular, we give a translation of a defeasible theory D into a meta-program P(D). We show that under a condition of decisiveness, the defeasible consequences of D correspond exactly to the sceptical conclusions of P(D) under the stable model semantics. Without decisiveness, the result holds only in one direction (all defeasible consequences of D are included in all stable models of P(D)). If we wish a complete embedding for the general case, we need to use the Kunen semantics of P(D), instead.

AB - Defeasible reasoning is a simple but efficient approach to nonmonotonic reasoning that has recently attracted considerable interest and that has found various applications. Defeasible logic and its variants are an important family of defeasible reasoning methods. So far no relationship has been established between defeasible logic and mainstream nonmonotonic reasoning approaches. In this paper we establish close links to known semantics of logic programs. In particular, we give a translation of a defeasible theory D into a meta-program P(D). We show that under a condition of decisiveness, the defeasible consequences of D correspond exactly to the sceptical conclusions of P(D) under the stable model semantics. Without decisiveness, the result holds only in one direction (all defeasible consequences of D are included in all stable models of P(D)). If we wish a complete embedding for the general case, we need to use the Kunen semantics of P(D), instead.

KW - Defeasible logic

KW - Kunen semantics

KW - Non-monotonic logic

KW - Stable semantics

UR - http://www.scopus.com/inward/record.url?scp=33750335026&partnerID=8YFLogxK

U2 - 10.1017/S1471068406002778

DO - 10.1017/S1471068406002778

M3 - Article

VL - 6

SP - 703

EP - 735

JO - Theory and Practice of Logic Programming

JF - Theory and Practice of Logic Programming

SN - 1471-0684

IS - 6

ER -