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The above definition takes a particular view on the formalization of the role of the integrity constraints <math>\mathit{IC}</math> as restrictions on the possible abductive solutions. It requires that these are entailed by the logic program extended with an abductive solution, thus meaning that in any model of the extended logic program (which one can think of as an ensuing world given <math>\Delta</math>) the requirements of the integrity constraints are met. In some cases this may be unnecessarily strong and the weaker requirement of consistency, namely that <math>P \cup \mathit{IC} \cup \Delta</math> is consistent, can be sufficient, meaning that there exists at least one model (possible ensuing world) of the extended program where the integrity constraints hold. In practice, in many cases these two ways of formalizing the role of the integrity constraints coincide as the logic program and its extensions always have a unique model. Many of the ALP systems use the entailment view of the integrity constraints as this can be easily implemented without the need for any extra specialized procedures for the satisfaction of the integrity constraints since this view treats the constraints in the same way as the problem goal.
==Implementation and systems==
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