Using Abduction to Compute Efficient Proofs

The aim of this work is to show how to compute an extra hypothesis H to an unproved sequent @C@?^?G, such that:*@C,H@?G is provable; *H is not trivial. *If @C@?G (which is not known a priory) then @C,H@?G has a much simpler proof. Due to the last item, this is not exactly the usual abductive reasoning found in literature, for the latter requires the input sequent not to be derivable. The idea is that @C is a contextual database, containing background knowledge, G is a goal formula representing some fact or evidence that one wants to explain or prove, and H is an hypothesis that explains the evidence in the presence of the background knowledge or that facilitates the proof of G from @C. We show how this task is related to the problem of computing non-analytic cuts. Several algorithms are provided that compute efficient proofs with non-analytic cuts via abductive reasoning. This is a joint work with Marcello D'Agostino and Dov Gabbay.