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The authors present the CIFF proof procedure for abductive logic programming with constraints, and they prove its correctness. CIFF is an extension of the IFF proof procedure for abductive logic programming, relaxing the original restrictions over variable quantification (allowedness conditions) and incorporating a constraint solver to deal with numerical constraints as in constraint logic programming. Finally, they describe the CIFF System, comparing it with state of the art abductive systems and answer set solvers and showing how to use it to program some applications.
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