A Necessary Condition for Constructive Negation in Constraint Logic Programming

Stuckey (1995) has presented a sound and complete procedure for Constructive Negation in Constraint Logic Programming, together with a sufficient condition, called admissible closure, which guarantees an effective implementation. In this paper we analyze this condition and relate it to the decidability of the underlying constraint structure. We prove that the admissible closure condition is also necessary to guarantee the existence of an effective implementation of Constructive Negation.