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→Example 3: Typo Tags: Mobile edit Mobile web edit |
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This definition leaves open the choice of the underlying semantics of logic programming through which we give the exact meaning of the entailment relation <math>\models</math> and the notion of consistency of the (extended) logic programs. Any of the different semantics of logic programming such as the completion, stable or well-founded semantics can (and have been used in practice) to give different notions of abductive explanations and thus different forms of ALP frameworks.
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.
In many practical cases, the third condition in this formal definition of an abductive explanation in ALP is either trivially satisfied or it is contained in the second condition via the use of specific integrity constraints that capture consistency.
==Implementation and systems==
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