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Independence of selecting rule and ordering rule in PT-resolution

Resolution with partial intersection and truncation (PT-resolution) has been introduced as a new derivation strategy in logic programming. A significant advantage of the resolution is that it prevents some derivations from infinite recursion. This paper concentrates on the independence of the selecting rule and ordering rule of PT-resolution. It is proven that a PT-derivation is independent from the selecting rule and that a PT-derivation is independent from the ordering rule.