ルールの本体での置換と一般の公理に関する証明手続きによる論理プログラムの計算手続きの完全性

抄録

In this paper, a logic program is considered as the union of a set of rules and an axiom which defines basic predicates and functions, and a procedure to calculate logic programs is considered as the combination of a replacement procedure with the bodies of the rules and a proof procedure with respect to the axiom. It is proved that a goal is a logical consequence of Δ ∪ Γ if and only if there exists n such that the logical formula obtained by replacing atomic formulae in the goal n times is a logical consequence of Δ, where Γ is the set of the rules, and Δ is the axiom. Moreover, conditions concerning Γ and Δ are described.