Combining Logic Programming and Equation Solving

Conditional equational theories can be built into logic programming using a generalized resolution rule which calls a universal uniication procedure. Such uniication procedures are often deened by sound and strongly complete sets of inference rules. In other words, to resolve upon two atoms requires to show-by means of the inference rules-that the corresponding arguments of the atoms are equal under a given equational theory. In this sense, derivations with respect to resolution and the inference rules are controlled by a xed computation rule. However, since the uniication problem is undecidable for many classes of equational theories this xed computation rule has several drawbacks. We show that refutations with respect to resolution and sound and strongly complete sets of inference rules for conditional equational theories are independent of a computation rule. Hence, resolution and equation solving can be performed on the same level.