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Unfounded Sets and Well-Founded Semantics for General Logic Programs.

Allen Van Gelder, Kenneth A. Ross, John S. Schlipf: Unfounded Sets and Well-Founded Semantics for General Logic Programs. PODS 1988: 221-230
@inproceedings{DBLP:conf/pods/GelderRS88,
  author    = {Allen Van Gelder and
               Kenneth A. Ross and
               John S. Schlipf},
  editor    = {Chris Edmondson-Yurkanan and
               Mihalis Yannakakis},
  title     = {Unfounded Sets and Well-Founded Semantics for General Logic Programs},
  booktitle = {Proceedings of the Seventh ACM SIGACT-SIGMOD-SIGART Symposium
               on Principles of Database Systems, March 21-23, 1988, Austin,
               Texas, USA},
  publisher = {ACM},
  year      = {1988},
  isbn      = {0-89791-263-2},
  pages     = {221-230},
  ee        = {http://doi.acm.org/10.1145/308386.308444, db/conf/pods/GelderRS88.html},
  crossref  = {DBLP:conf/pods/88},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}

Abstract

A general logic program (abbreviated to "program hereafter) is a set of rules that have both positive and negative subgoals. It is common to view a deductive database as a general logic program consisting of rules (IDB) sitting above elementary relations (EDB, facts). It is desirable to associate one Herbrand model with a program and think of that model as the "meaning of the program," or its "declarative semantics." Ideally, queries directed to the program would be answered in accordance with this model. We introduce unfounded sets and well-founded partial models, and define the well-founded semantics of a program to be its well- founded partial model. If the well-founded partial model is in fact a model, we call it the well-founded model, and say the program is "well-behaved". We show that the class of well-behaved programs properly includes previously studied classes of "stratified" and "locally stratified" programs. Gelfond and Lifschitz have proposed a definition of "unique stable model" for general logic programs. We show that a program has a unique stable model if it has a well-founded model, in which case they are the same. We discuss why the converse is not true.

Copyright © 1988 by the ACM, Inc., used by permission. Permission to make digital or hard copies is granted provided that copies are not made or distributed for profit or direct commercial advantage, and that copies show this notice on the first page or initial screen of a display along with the full citation.

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Printed Edition

Chris Edmondson-Yurkanan, Mihalis Yannakakis (Eds.): Proceedings of the Seventh ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, March 21-23, 1988, Austin, Texas, USA. ACM 1988, ISBN 0-89791-263-2
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Online Edition: ACM Digital Library

Journal Version

Allen Van Gelder, Kenneth A. Ross, John S. Schlipf: The Well-Founded Semantics for General Logic Programs. J. ACM 38(3): 620-650(1991) CiteSeerX Google scholar pubzone.org BibTeX bibliographical record in XML

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