Shielded base contraction

Abstract The one that is considered the standard model in the area of logic of belief change was proposed by Alchourron, Gardenfors and Makinson in 1985 and is, nowadays, known as the AGM model. Two of the main shortcomings pointed out to the AGM model of belief change are the (impractical) use of belief sets to represent belief states and the (unrealistic) acceptance of any new information. In this paper we study a kind of operators—known as shielded base contractions—which address both those issues. Indeed, on the one hand, these operators are defined on belief bases (rather than belief sets) and, on the other hand, they are constructed with the underlying idea that not all new informations are accepted. We propose twenty different classes of shielded base contractions and obtain axiomatic characterizations for each of them. Additionally we thoroughly investigate the interrelations (in the sense of inclusion) among all those classes. More precisely, we analyse whether each of those classes is or is not (strictly) contained in each of the remaining ones.