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Three-Valued Formalization of Logic Programming: Is It Needed?

Jia-Huai You, Li-Yan Yuan: Three-Valued Formalization of Logic Programming: Is It Needed? PODS 1990: 172-182
@inproceedings{DBLP:conf/pods/YouY90,
  author    = {Jia-Huai You and
               Li-Yan Yuan},
  title     = {Three-Valued Formalization of Logic Programming: Is It Needed?},
  booktitle = {Proceedings of the Ninth ACM SIGACT-SIGMOD-SIGART Symposium on
               Principles of Database Systems, April 2-4, 1990, Nashville, Tennessee},
  publisher = {ACM Press},
  year      = {1990},
  isbn      = {0-89791-352-3},
  pages     = {172-182},
  ee        = {http://doi.acm.org/10.1145/298514.298559, db/conf/pods/YouY90.html},
  crossref  = {DBLP:conf/pods/90},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}
BibTeX

Abstract

The central issue of this paper concerns the truth value undefined in Przymusinsi's 3-valued formalization of nonmonotonic reasoning and logic programming. We argue that this formalization can lead to the problem of unintended semantics and loss of disjunctive information. We modify the formalization by proposing two general principles for logic program semantics: justifiability and minimal undefinedness. The former is shown to be a general property for almost all logic program semantics, and the latter requires the use of the undefined only when it is necessary. We show that there are three types of information embedded in the undefined: the disjunctive, the factoring, and the "difficult-to-be-assigned". In the modified formalization, the first two can be successfully identified and branched into multiple models. This leaves only the "difficult-to-be-assigned" as the undefined. It is shown that the truth value undefined is needed only for a very special type of programs whose practicality is yet to be evidenced.

Copyright © 1990 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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Proceedings of the Ninth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, April 2-4, 1990, Nashville, Tennessee. ACM Press 1990, ISBN 0-89791-352-3
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References

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[2]
François Bry: Logic Programming as Constructivism: A Formalization and its Application to Databases. PODS 1989: 34-50 BibTeX
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[4]
Phan Minh Dung, Kanchana Kanchanasut: A Fixpoint Approach to Declarative Semantics of Logic Programs. NACLP 1989: 604-625 BibTeX
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Melvin Fitting: A Kripke-Kleene Semantics for Logic Programs. J. Log. Program. 2(4): 295-312(1985) BibTeX
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Michael Gelfond, Vladimir Lifschitz: The Stable Model Semantics for Logic Programming. ICLP/SLP 1988: 1070-1080 BibTeX
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Kenneth Kunen: Negation in Logic Programming. J. Log. Program. 4(4): 289-308(1987) BibTeX
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V. Wiktor Marek, V. S. Subrahmanian: The Relationship Between Logic Program Semantics and Non-Monotonic Reasoning. ICLP 1989: 600-617 BibTeX
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Halina Przymusinska, Teodor C. Przymusinski: Weakly Perfect Model Semantics for Logic Programs. ICLP/SLP 1988: 1106-1120 BibTeX
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Teodor C. Przymusinski: Perfect Model Semantics. ICLP/SLP 1988: 1081-1096 BibTeX
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Teodor C. Przymusinski: Three-Valued Formalizations of Non-Monotonic Reasoning and Logic Programming. KR 1989: 341-348 BibTeX
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Teodor C. Przymusinski: Every Logic Program Has a Natural Stratification And an Iterated Least Fixed Point Model. PODS 1989: 11-21 BibTeX
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Allen Van Gelder, Kenneth A. Ross, John S. Schlipf: Unfounded Sets and Well-Founded Semantics for General Logic Programs. PODS 1988: 221-230 BibTeX
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Allen Van Gelder: The Alternating Fixpoint of Logic Programs with Negation. PODS 1989: 1-10 BibTeX
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Jia-Huai You, Liwu Li: Supported Circumscription and Its Relation to Logic Programming with Negation. NACLP 1989: 291-309 BibTeX
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Jia-Huai You, Li-Yan Yuan: A Three-Valued Semantics for Deductive Databases and Logic Programs. J. Comput. Syst. Sci. 49(2): 334-361(1994) BibTeX
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Referenced by

  1. Domenico Saccà: Deterministic and Non-Deterministic Stable Model Semantics for Unbound DATALOG Queries. ICDT 1995: 353-367
  2. Catriel Beeri, Raghu Ramakrishnan, Divesh Srivastava, S. Sudarshan: The Valid Model Semantics for Logic Programs. PODS 1992: 91-104
  3. Domenico Saccà, Brigitte Verdonk, Dirk Vermeir: Evolution of Knowledge Bases. EDBT 1992: 230-244
  4. Els Laenens, Dirk Vermeir: On the Relationship between Well-Founded and Stable Partial Models. MFDBS 1991: 59-73
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