Surviving abduction

Abduction or retroduction, as introduced by C. S. Peirce in the double sense of searching for explanatory instances and providing an explanation (i.e., involving the procedure of searching, and the function of providing an explanans to the explanandum) is a kind of complement for usual argumentation. There is, however, an inferential step from the explanandum to the (one or more) abductive explanans (that is, to the facts that will explain it). Whether this inferential step can be captured by logical machinery depends upon a number of assumptions, but in any case it suffers in principle from the triviality objection: any time a singular contradictory explanans occurs, the system collapses and stops working. The traditional remedies for such collapsing are the expensive (indeed, NP-complete) mechanisms of consistency maintenance, or complicated theories of non-monotonic derivation that keep the system running at a higher cost. I intend to show that the robust logics of formal inconsistency, a particular category of paraconsistent logics which permit the internalization of the concepts of consistency and inconsistency inside the object language, provide simple yet powerful techniques for automatic abduction. Moreover, the whole procedure is capable of automatization by means of the tableau proof-procedures available for such logics. Some motivating examples are discussed in detail.