Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Minimum model semantics for logic programs with negation-as-failure

Minimum model semantics for logic programs with negation-as-failure We give a purely model-theoretic characterization of the semantics of logic programs with negation-as-failure allowed in clause bodies. In our semantics, the meaning of a program is, as in the classical case, the unique minimum model in a program-independent ordering. We use an expanded truth domain that has an uncountable linearly ordered set of truth values between False (the minimum element) and True (the maximum), with a Zero element in the middle. The truth values below Zero are ordered like the countable ordinals. The values above Zero have exactly the reverse order. Negation is interpreted as reflection about Zero followed by a step towards Zero ; the only truth value that remains unaffected by negation is Zero . We show that every program has a unique minimum model M P , and that this model can be constructed with a T P iteration which proceeds through the countable ordinals. Furthermore, we demonstrate that M P can alternatively be obtained through a construction that generalizes the well-known model intersection theorem for classical logic programming. Finally, we show that by collapsing the true and false values of the infinite-valued model M P to (the classical) True and False , we obtain a three-valued model identical to the well-founded one. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Computational Logic (TOCL) Association for Computing Machinery

Minimum model semantics for logic programs with negation-as-failure

Loading next page...
 
/lp/association-for-computing-machinery/minimum-model-semantics-for-logic-programs-with-negation-as-failure-hpECWyo4sc

References (34)

Publisher
Association for Computing Machinery
Copyright
Copyright © 2005 by ACM Inc.
ISSN
1529-3785
DOI
10.1145/1055686.1055694
Publisher site
See Article on Publisher Site

Abstract

We give a purely model-theoretic characterization of the semantics of logic programs with negation-as-failure allowed in clause bodies. In our semantics, the meaning of a program is, as in the classical case, the unique minimum model in a program-independent ordering. We use an expanded truth domain that has an uncountable linearly ordered set of truth values between False (the minimum element) and True (the maximum), with a Zero element in the middle. The truth values below Zero are ordered like the countable ordinals. The values above Zero have exactly the reverse order. Negation is interpreted as reflection about Zero followed by a step towards Zero ; the only truth value that remains unaffected by negation is Zero . We show that every program has a unique minimum model M P , and that this model can be constructed with a T P iteration which proceeds through the countable ordinals. Furthermore, we demonstrate that M P can alternatively be obtained through a construction that generalizes the well-known model intersection theorem for classical logic programming. Finally, we show that by collapsing the true and false values of the infinite-valued model M P to (the classical) True and False , we obtain a three-valued model identical to the well-founded one.

Journal

ACM Transactions on Computational Logic (TOCL)Association for Computing Machinery

Published: Apr 1, 2005

There are no references for this article.