## Well-Founded Semantics Coincides with Three-Valued Stable Semantics (1990)

Venue: | Fundamenta Informaticae |

Citations: | 138 - 15 self |

### BibTeX

@ARTICLE{Przymusinski90well-foundedsemantics,

author = {Teodor Przymusinski},

title = {Well-Founded Semantics Coincides with Three-Valued Stable Semantics},

journal = {Fundamenta Informaticae},

year = {1990},

volume = {13},

pages = {445--463}

}

### Years of Citing Articles

### OpenURL

### Abstract

We introduce 3-valued stable models which are a natural generalization of standard (2-valued) stable models. We show that every logic program P has at least one 3-valued stable model and that the wellfounded model of any program P [VGRS90] coincides with the smallest 3-valued stable model of P. We conclude that the well-founded semantics of an arbitrary logic program coincides with the 3-valued stable model semantics. The 3-valued stable semantics is closely related to non-monotonic formalisms in AI. Namely, every program P can be translated into a suitable autoepistemic (resp. default) theory P so that the 3-valued stable semantics of P coincides with the (3-valued) autoepistemic (resp. default) semantics of P . Similar results hold for circumscription and CWA. Moreover, it can be shown that the 3-valued stable semantics has a natural extension to the class of all disjunctive logic programs and deductive databases. The author acknowledges support from the National Science Foundat...

### Citations

1913 | Foundations of Logic Programming - LLoyd - 1987 |

1550 | The stable model semantics for logic programming
- Gelfond, Lifschitz
- 1988
(Show Context)
Citation Context ...ently, D. S. Warren introduced the Extended Warren Abstract Machine (XWAM) for this semantics [War89] and developed an elegant interpreter in Prolog. The stable model semantics has been introduced in =-=[GL88]-=- (see also [BF88]). It is a 2-valued semantics, which also extends the perfect model semantics and has an elegant and simple fixed point definition. It is closely related to autoepistemic and default ... |

977 | Negation as failure - Clark - 1978 |

875 | The well-founded semantics for general logic programs
- Gelder, Ross, et al.
- 1991
(Show Context)
Citation Context ...dels which are a natural generalization of standard (2-valued) stable models. We show that every logic program P has at least one 3-valued stable model and that the wellfounded model of any program P =-=[VGRS90]-=- coincides with the smallest 3-valued stable model of P. We conclude that the well-founded semantics of an arbitrary logic program coincides with the 3-valued stable model semantics. The 3-valued stab... |

734 | Predicate logic as programming language
- Kowalski
- 1974
(Show Context)
Citation Context ...in [GL88]. Every 2-valued stable model is a 3-valued stable model, so our definition extends the notion of stable models. First, we need the following generalization of the Kowalski-Van Emden Theorem =-=[VEK76]-=-: Theorem 3.1 Every positive logic program P has a unique least 3-valued model. The above theorem is a strict generalization of the Kowalski-Van Emden theorem in view of the fact that our positive log... |

635 | Towards a theory of declarative knowledge - Apt, Blair, et al. - 1988 |

391 | A Kripke-Kleene Semantics for Logic Programs - Fitting - 1985 |

343 |
Logic programs with classical negation
- Gelfond, Lifschitz
- 1990
(Show Context)
Citation Context ...dence that b holds. This is much weaker than the requirement of positive evidence that the negation :b of b holds, which is needed to assert classical negation of b. Gelfond and Lifschitz pointed out =-=[GL89] tha-=-t in logic programming it is often useful to use the negation as failure operator (��) together with a different negation operator (:), which is supposed to constitute a rough counterpart of class... |

240 | Negation in logic programming - Kunen - 1985 |

216 | The alternating fixpoint of logic programs with negation - GELDER - 1989 |

143 | Every logic program has a natural stratification and an iterated least fixed point model
- Przymusinski
- 1989
(Show Context)
Citation Context ...iding various drawbacks of the other proposed approaches (see [PP90] for an overview). The wellfounded semantics has been proven to share many of the natural properties of the perfect model semantics =-=[Prz89a]-=- and it has been shown to be equivalent to suitable (3-valued) forms of all four major non-monotonic formalisms [Prz91, Prz89b]. Recently, D. S. Warren introduced the Extended Warren Abstract Machine ... |

132 | Negation as failure using tight derivations for general logic programs - Gelder - 1988 |

111 |
On Stratified Autoepistemic Theories
- Gelfond
- 1987
(Show Context)
Citation Context ...tics of P coincides with the (3-valued) autoepistemic (resp. default) semantics ofsP [Prz91]. We first need to translate logic programs into autoepistemic theories. We use the translation proposed in =-=[Gel87]-=-. Definition 5.1 [Gel87] Let P be a logic program. The autoepistemic theory P , which we call the autoepistemic translation of P , consists of all clauses of the form: A / B 1 ; : : : ; Bm ; :LC 1 ; :... |

96 |
Extended stable semantics for normal and disjunctive programs
- Przymusinski
- 1990
(Show Context)
Citation Context ...alued stable semantics to non-monotonic formalisms. In Section 6 we extend our results to programs permitting the use of both negations �� and :. The results contained in this paper were announced=-= in [Prz90a]-=-. The extension of the 3-valued stable semantics to all disjunctive programs is described in [Prz90a, Prz90b]. For an overview of semantic issues in logic programming and theory of deductive databases... |

69 | On the declarative semantics of stratified deductive databases and logic programs - Przymusinski - 1988 |

64 |
General logical databases and programs: Default logic, semantics and stratification
- Bidoit, Froidevaux
- 1991
(Show Context)
Citation Context ...en introduced the Extended Warren Abstract Machine (XWAM) for this semantics [War89] and developed an elegant interpreter in Prolog. The stable model semantics has been introduced in [GL88] (see also =-=[BF88]-=-). It is a 2-valued semantics, which also extends the perfect model semantics and has an elegant and simple fixed point definition. It is closely related to autoepistemic and default approaches to non... |

58 |
Stationary semantics for disjunctive logic programs and deductive databases
- Przymusinski
- 1990
(Show Context)
Citation Context ...sjunctive logic programs and deductive databases. The fact that the 3-valued stable semantics is well-defined for any normal program and can be extended to the class of all disjunctive logic programs =-=[Prz90b]-=- is very important. A logic program may contain predicates whose truth or falsity is not fully determined by the program (and thus is undefined), in addition to predicates whose truth value is complet... |

54 | Semantic issues in deductive databases and logic programs
- Przymusinska, Przymusinski
- 1990
(Show Context)
Citation Context ... of the perfect model semantics [ABW88, VG89b, Prz88a] from the class of stratified logic programs to the class of all logic programs, avoiding various drawbacks of the other proposed approaches (see =-=[PP90]-=- for an overview). The wellfounded semantics has been proven to share many of the natural properties of the perfect model semantics [Prz89a] and it has been shown to be equivalent to suitable (3-value... |

53 | Stable and extension class theory for logic programs and default theories - BARAL, SUBRAHMANIAN - 1992 |

36 | Logic programming as constructivism: A formalization and its application to databases - Bry - 1989 |

35 | Three-valued non-monotonic formalisms and semantics of logic programs
- Przymusinski
- 1991
(Show Context)
Citation Context ...very program P can be translated into an autoepistemic (resp. default) theory P , so that the 3-valued stable semantics of P coincides with the (3-valued) autoepistemic (resp. default) semantics of P =-=[Prz91]-=-. Similar results hold for circumscription and CWA. In [Prz90a, Prz90b] we prove that the 3-valued stable semantics has a natural extension to the class of all disjunctive logic programs, thus providi... |

25 | Generalized well-founded semantics for logic programs
- Baral, Lobo, et al.
- 1990
(Show Context)
Citation Context ...ioned before, the above program does not have any 2-valued stable models. It also illustrates differences between the 3-valued stable (well-founded) semantics and the semantics recently introduced in =-=[BLM90], wh-=-ich implies, e.g., work sleep and generally treats clauses of the form A / ��B as disjunctions AsB, which our semantics does not do. In general, a logic program may have more than one 3-valued sta... |

18 | Non-monotonic formalisms and logic programming - Przymusinski - 1989 |

13 | The XWAML: A machine that integrates Prolog and deductive database query evaluation - Warren - 1989 |

9 | C.: On the relationship between nonmonotonic reasoning and logic programming - Przymusinski - 1988 |