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Generalization as described before is applied to the clauses of a theory, i.e. facts and rules, resulting in more general rules. We have also developed a new technique for abduction. In addition to the Horn-clause theory consisting of facts and rules and a set of integrity constraints IC. we also postulate a set of distinguished ground literals called abducibles and a goal which drives the abduction process.

By abduction we want to find a set of hypotheses such that we can derive the (positive) example from . In the context of theory revision gives the new theory which again must be consistent with IC, the set of integrity constraints:

is consistent

Consider the following example where we have two rules for the recyclability of polypropylenes:

polypropylene(Plastic_Id), additive(Plastic_Id,flame-retardent)
polypropylene(Plastic_Id), pure(Plastic_Id)
polypropylene(X) hostalen (X)
The first rule expresses that a polypropylene can be recycled only in a closed circle, if it contains a flame retardent agent as a fluent additive. This is because the flame retardent agent produces toxic dioxin on ultimate thermic treatment. For a pure polypropylene there is no restriction a recyclability. In two facts we also have that hostalen ppk_1060 contains a flame retardent fluent additive.

If we declare additive and pure as abducibles and ask the query how ppk_1060 can be recycled

?- recyclable(RecKind,ppk_1060)
we get two answers: The first, unconditional answer
RecKind = closed_circle
says that ppk_1060 can be recycled in a closed circle. The second, conditional answer
RecKind = unrestricted
is an abductive solution: under the condition that ppk_1060 is pure, it can be recycled unrestricted.

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Harold Boley, Stefani Possner, Franz Schmalhofer (