Abductive Reasoning : Backward and Forward

We propose to reconsider abductive reasonning in the context of empirical reasonning, and to investigate its deep relations with constraint-based reasonning, a currently very success-full approach used in the problem-solving community. Abduction has been proposed in the rst years of this century by the logician and philosopher C. S. Peirce as a new inference mechanism for logical system along induction and deduction 16]. To quote Peirce himself (Collected Papers, 6.524) : \ The rst starting of a hypothesis and the entertaining of it, whether as a simple interrogation or with any degree of conndence, is an inferential step which I propose to call abduction (or retroduction)." The alternative denomination of "retroduction", that have been rst used by Peirce in 1898 and abandonned circa 1901, shows well the fact that the key issue in abduction is to go back from the facts to the hypotheses. But abduction is more than that and it diiers form induction because it accounts for a second forward step from the hypotheses to the facts, as Peirce explained (Collected Papers , 6.525) : \Long before I rst classed abduction as an inference it was recognized by logicians that the operation of adopting an explanatory hypothesis { which is just what abduction is { was subject to certain conditions. Namely, the hypothesis cannot be admitted, even as an hypothesis, unless it be supposed that it would account for the facts or some of them. The form of inference , therefore, is this : the surprising fact, C, is observed; But if A were true, C would be a matter of course, Hence, there is reason to suspect that A is true." It seems however that the premisses of ab-ductive reasoning can be traced back to the XVIIth century in the logical writings of G. W. Leibniz, who was the rst to notice the insuu-ciency of the traditional (Aristotelian) modes of reasoning, either purely deductive (analytic) or purely inductive (synthetic). Louis Couturat, in his study of Leibniz's logic 6], pointed out that Leibniz was trying to deene a new mechanism for hypothesis formation that would take from both induction and deduction. Leibniz was indeed interested in deening a very uniform methodology for a universal science that would apply to both exact and experimental sciences. He considered that induction alone cannot be suucient for explaining new facts or experiments, and could even lead sometimes to wrong conclusions. Hypotheses have …