Aggregation and negationasfailure
 Mauricio Osorio,
 Bharat Jayaraman
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Setgrouping and aggregation are powerful operations of practical interest in database query languages. An aggregate operation is a function that maps a set to some value, e.g., the maximum or minimum in the set, the cardinality of this set, the summation of all its members, etc. Since aggregate operations are typically nonmonotonic in nature, recursive programs making use of aggregate operations must be suitably restricted in order that they have a welldefined meaning. In a recent paper we showed that partialorder clauses provide a wellstructured means of formulating aggregate operations with recursion. In this paper, we consider the problem of expressing partialorder programs via negationasfailure (NF), a wellknown nonmonotonic operation in logic programming. We show a natural translation of partialorder programs to normal logic programs: Anycostmonotonic partialorder programsP is translated to astratified normal program such that the declarative semantics ofP is defined as the stratified semantics of the translated program. The ability to effect such a translation is significant because the resulting normal programs do not make any explicit use of theaggregation capability, yet they are concise and intuitive. The success of this translation is due to the fact that the translated program is a stratified normal program. That would not be the case for other more general classes of programs thancostmonotonic partialorder programs. We therefore develop in stages a refined translation scheme that does not require the translated programs to be stratified, but requires the use of a suitable semantics. The class of normal programs originating from this refined translation scheme is itself interesting: Every program in this class has a clear intended total model, although these programs are in general neither stratified nor callconsistent, and do not have a stable model. The partial model given by the wellfounded semantics is consistent with the intended total model and the extended well founded semantics,WFS ^{+}, defines the intended model. Since there is a welldefined and efficient operational semantics for partialorder programs^{14, 15, 21)} we conclude that the gap between expression of a problem and computing its solution can be reduced with the right level of notation.
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 Title
 Aggregation and negationasfailure
 Journal

New Generation Computing
Volume 17, Issue 3 , pp 255284
 Cover Date
 19990901
 DOI
 10.1007/BF03037222
 Print ISSN
 02883635
 Online ISSN
 18827055
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Aggregation
 NegationAsFailure
 Well Founded Semantics
 Partial Order Clauses
 Database Query Languages
 Declarative Programming
 Deductive Databases
 Industry Sectors
 Authors

 Mauricio Osorio ^{(1)}
 Bharat Jayaraman ^{(2)}
 Author Affiliations

 1. Departamento de Ingenieria en Sistemas Computacionales, Universidad de las Americas, Sta. Catarina Martir, Cholula, 72820, Puebla, Mexico
 2. Department of Computer Science and Engineering, State University of New York at Buffalo, 14260, Buffalo, NY, U.S.A.