Explanatory relations revisited: Links with credibility-limited revision

Abstract

We study binary relations ⊳ over propositional formulas built over a finite set of variables. The meaning of α ⊳ γ is that γ is a preferred explanation of the observation α. These relations are called Explanatory or abductive relations. We find two important families of abductive relations characterized by his axiomatic behavior: the ordered explanatory relations and the weakly reflexive explanatory relations. We show that both families have tight links with the framework of Credibility limited revision. These relationships allow to establish semantical representations for each family. An important corollary of our representations results is that our axiomatizations allow us to overcome the background theory present in most axiomatizations of abduction.