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

Venue: | Fundamenta Informaticae |

Citations: | 139 - 17 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...