### Citations

965 |
Circumscriptionâ€”a form of non-monotonic reasoning.
- McCarthy
- 1980
(Show Context)
Citation Context ...cription for well-founded theories. 1 Introduction Circumscription is proposed by McCarthy [6] as a possible solution for the qualification problem in AI. He later introduced predicate circumscription=-=[7]-=- as a generalization of previous version which he called domain circumscription. Given a theory T and a set of predicates P, predicate circumscription minimizes the extensions of P that satisfy T. The... |

340 | Pointwise circumscription.
- Lifschitz
- 1986
(Show Context)
Citation Context ...r discussion is restricted to single predicate circumscription, we give the two definitions below for a single predicate whereas they are originally for multiple predicates. Definition 1.3 (Lifschitz =-=[5]-=-) A theory T is well-founded w.r.t (P; Z) if for each model A of T, there exists a (P; Z)-minimal model B such that BsT P; Z A. However, there are perfectly reasonable theories, such as the simple the... |

168 | Epistemological problems of Artificial Intelligence. In
- McCarthy
- 1977
(Show Context)
Citation Context ...uces sensible results. Therefore, these new definitions also coincide with the original definition of circumscription for well-founded theories. 1 Introduction Circumscription is proposed by McCarthy =-=[6]-=- as a possible solution for the qualification problem in AI. He later introduced predicate circumscription[7] as a generalization of previous version which he called domain circumscription. Given a th... |

35 |
On the Adequacy of Predicate Circumscription for Closedworld Reasoning.
- Etherington, Mercer, et al.
- 1985
(Show Context)
Citation Context ... A of T, there exists a (P; Z)-minimal model B such that BsT P; Z A. However, there are perfectly reasonable theories, such as the simple theory of natural successor (the example given in Etherington =-=[3]-=-), that are not well-founded. Another approach to the same problem is to weaken circumscription by generalizing the minimality criterion which will accordingly increase the class of theories that can ... |

32 |
The mathematics of non-monotonic reasoning
- Davis
- 1980
(Show Context)
Citation Context ...Predicate Circumscription The original definition of circumscription is based on minimal models. However, if a theory has no minimal models, then circumscribing it gives an inconsistent theory. Davis =-=[1]-=- and Etherington [3] provide examples of such theories for domain and predicate circumscription, respectively. Liau et. al. [4] presents Etherington's example and shows how their definition of abstrac... |

1 |
Abstract minimality and circumscription
- Liau, Lin
- 1992
(Show Context)
Citation Context ...same problem is to weaken circumscription by generalizing the minimality criterion which will accordingly increase the class of theories that can be consistently handled. Definition 1.4 (Liau et. al. =-=[4]-=-) Given a theory T, a model A of T is abstractly (P; Z)-minimal if for each model BsT P; Z A, B = A. Since a theory can have abstractly minimal models without having minimal models (i.e., theory of su... |