A Procedure to Calculate Logic Programs by Replacement with the Bodies of Rules and Transformation to Disjunctive Normal Forms

In this paper, we describe the completeness of a calculation procedure of logic programs. The procedure is the combination of two procedures, a replacement procedure of atoms in the goal by the bodiesor the negation of the bodies of rules in the program, and a transformation procedure of equations t...

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Bibliographic Details
Published inTransactions of the Japanese Society for Artificial Intelligence Vol. 19; no. 5; pp. 413 - 420
Main Authors Akiba, Sumitaka, Sato, Taisuke
Format Journal Article
LanguageJapanese
Published The Japanese Society for Artificial Intelligence 2004
Subjects
Clark's equational theory (CET)
disjunctive normal form (DNF)
three-valued logic
ultraproduct
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Summary:In this paper, we describe the completeness of a calculation procedure of logic programs. The procedure is the combination of two procedures, a replacement procedure of atoms in the goal by the bodiesor the negation of the bodies of rules in the program, and a transformation procedure of equations to disjunctivenormal forms (DNF) equivalent under Clark's EquationalTheory (CET). To combine replacement of atoms in the goal to logicalformulae determined from the program and transformation ofequations to DNF equivalent under CET is a method by whichprocedures with the capability of expressing answers in DNFcan be build, so it is a leading method for expressing answers in a formincluding negation. Some procedures based on the method are devised, and their calculation capabilities are shown by applying thetheory of completed programs. However, the procedure that uses the bodies or the negation of thebodies of rules for replacement has higher calculationcapability, and is intuitively more natural than they. Therefore, to clarify the calculation capability of theprocedure is considered an important subject for researchinto calculation procedures of logic programs with thecapability for expressing answers in a form includingnegation. Moreover, since the completeness is realized by standing on theviewpoint of treating the implication symbol as a differentimplication symbol from usual, and interpreting logic programs in three-valued logic, examples which support the viewpoint are also described.
ISSN:1346-0714
1346-8030
DOI:10.1527/tjsai.19.413