The Extended Closed World Assumpution and its Relationship to Parallel Circumscription.

@inproceedings{DBLP:conf/pods/GelfondPP86,
  author    = {Michael Gelfond and
               Halina Przymusinska and
               Teodor C. Przymusinski},
  title     = {The Extended Closed World Assumpution and its Relationship to
               Parallel Circumscription},
  booktitle = {Proceedings of the Fifth ACM SIGACT-SIGMOD Symposium on Principles
               of Database Systems, March 24-26, 1986, Cambridge, Massachusetts},
  publisher = {ACM},
  year      = {1986},
  isbn      = {0-89791-179-2},
  pages     = {133-139},
  ee        = {http://doi.acm.org/10.1145/6012.15410, db/conf/pods/GelfondPP86.html},
  crossref  = {DBLP:conf/pods/86},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}

Abstract

The aim of this paper is to investigate two powerful methods of handling negative information in logic-based knowledge representation systems: the negation as failure rule, formalized as the Closed World Assumption (CWA) by R. Reiter and the parallel circumscription introduced by J. McCarthy. Reiter's CWA is applicable only to definite theories; its extension to indefinite theories, called the Generalized Closed World Assumption (GCWA), has been proposed by J. Minker.

We argue that Minker's GCWA can be further modified in two different directions. First of all, the class of formulas which can be added to our initial set of beliefs can be expanded by including negations of non-atomic formulas. Secondly, the negation as failure rule can be applied not only to all predicates, but to an arbitrary list of predicates.

We extend GCWA in both directions and construct a system called the Extended Closed World Assumption (ECWA). We prove that under certain natural constraints on the set of beliefs, ECWA is equivalent to parallel circumscription, thereby showing that the negation as failure rule can be considered as a particular case of circumscription. Our results also provide a description of the facts added to the initial theory by parallel circumscription.

Copyright © 1986 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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References

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Michael Gelfond, Halina Przymusinska: Negation as Failure: Careful Closure Procedure. Artif. Intell. 30(3): 273-287(1986) BibTeX

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John C. Shepherdson: Negation as Failure: A Comparison of Clark's Completed Data Base and Reiter's Closed World Assumption. J. Log. Program. 1(1): 51-79(1984) BibTeX

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Referenced by

1. Edward P. F. Chan: A Possible World Semantics for Disjunctive Databases. IEEE Trans. Knowl. Data Eng. 5(2): 282-292(1993)
2. José Alberto Fernández, Jack Minker: Semantics of Disjunctive Deductive Databases. ICDT 1992: 21-50
3. Stefan Brass: Beginnings of a Theory of General Database Completions. ICDT 1990: 349-363
4. Stefan Brass, Udo W. Lipeck: Specifying Closed World Assumptions for Logic Databases. MFDBS 1989: 68-84
5. Jeffrey D. Ullman: Principles of Database and Knowledge-Base Systems, Volume II. Computer Science Press 1989, ISBN 0-7167-8162-X
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