Abstract :

Abduction was first introduced by the philosopher C.S. Peirce in the epistemological context of scientific discovery. It was more recently analyzed in Artificial Intelligence, especially with respect to diagnosis analysis or ordinary reasoning. These two fields share a common view of abduction as a general process of hypotheses formation. More precisely, abduction is conceived as a kind of reverse explanation where a hypothesis H can be abduced from facts E if H is a "good explanation" of E. The paper aims at giving a general logical picture of abduction which could be used in both fields. The most standard way to define a good explanation is through deduction, "classical abduction" from E to H being then defined as reverse deduction: HÍE. Since such a definition can be shown to be unsatisfactory, a richer approach consists in introducing moreover a belief revision operation. In a semantic belief revision framework, an agent's initial belief K is revised into a final belief K*A when the agent receives some message A. Replacing H or E by the respective beliefs K*H or K*E leads naturally to three possible alternative schemes to reverse deduction. The paper studies these alternative schemes which are first evaluated through the intuitive relevance of their semantic definitions, considering the general heuristic that an abduction must be the reverse of a good explanation. Some examples which appear intuitively to be desirable or not are given to support our argumentation. Second, sets of axioms for the three altethe inversion of a consequence relation (either deductive or non monotonic). rnatives and proofs for the corresponding representation theorems are given. Third, the three alternatives are compared through the more or less strong axioms on which they rest. Finally, on semantic grounds as well as on axiomatic grounds, one abduction definition which was never vindicated by previous work is selected. This definition, named "ordered abduction" says that H is abduced from E if and only if K*HÍK*E . It leads to consider abduction as a logical relation which cannot be directly defined by the inversion of a consequence relation (either deductive or non monotonic).