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 (DNF) equivalent under Clark's Equational
Theory (CET).
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.
