Abstract

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 bodies or the negation of the bodies of rules in the program, and a transformation procedure of equations to disjunctive normal forms equivalent under Clark's Equational Theory. To combine replacement of atoms in the goal to logical formulae determined from the program and transformation of equations to DNF equivalent under CET is a method by which procedures with the capability of expressing answers in DNF can be build, so it is a leading method for expressing answers in a form including negation. Some procedures based on the method are devised, and their calculation capabilities are shown by applying the theory of completed programs. However, the procedure that uses the bodies or the negation of the bodies of rules for replacement has higher calculation capability, and is intuitively more natural than they. Therefore, to clarify the calculation capability of the procedure is considered an important subject for research into calculation procedures of logic programs with the capability for expressing answers in a form including negation. Moreover, since the completeness is realized by standing on the viewpoint of treating the implication symbol as a different implication symbol from usual, and interpreting logic programs in three-valued logic, examples which support the viewpoint are also described.