Completeness for cut-based abduction

In traditional abduction methods it is assumed that the goal data has not yet been explained. In first-order logic (FOL) such precondition is, in general, undecidable. To avoid this problem, it was presented in D'Agostino, Finger and Gabbay (2008, Logic J. of the IGPL, 16, 537–560) a first-order cut-based abduction method which has as underlying inference system the KE-tableaux. Such inference system is non-analytical and the method presented in D'Agostino, Finger and Gabbay (2008, Logic J. of the IGPL, 16, 537–560) generalizes the traditional abduction avoiding the undecidable precondition; its correctness was demonstrated. Here we will show the completeness of the method for both propositional and first-order logic.