"All's well that ends well" - a proposal of global abduction

This paper presents a new form of abduction called global abduction. Usual abduction in logic programming is used to complement unknown information and used in one derivation path in a search tree. We call this kind of abduction local abduction. In this paper, we propose another abduction which is used over paths in a search tree for search control. As far as we know, this is the first attempt to formalize a search control in a logical way. We discuss applications of global abduction by using examples; a formalization of don’t-care nondeterminism and a formalization of reuse of the previously obtained result in a different search path. Then, we give a correct proof procedure for global abduction. The correctness is defined as “all’s well that ends well” principle meaning that the results obtained from a global abduction proof procedure are exactly the same as the ones which are logically true from the augmented program with the last set of abduced atoms.