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We present the CIFF proof procedure for abductive logic programming withconstraints, and we prove its correctness. CIFF is an extension of the IFFproof procedure for abductive logic programming, relaxing the originalrestrictions over variable quantification (allowedness conditions) andincorporating a constraint solver to deal with numerical constraints as inconstraint logic programming. Finally, we describe the CIFF system, comparingit with state of the art abductive systems and answer set solvers and showinghow to use it to program some applications. (To appear in Theory and Practiceof Logic Programming - TPLP).

The CIFF Proof Procedure for Abductive Logic Programming with Constraints: Theory, Implementation and Experiments