Marco Garapa
The logic of theory change became a major subject in philosophical logic and artificial intelligence in the middle of the 1980’s. The AGM model of belief change was proposed by Alchourrón, Gärdenfors and Makinson and acquired the status of standard model of belief change. In this model the beliefs of an agent are represented by a set of sentences closed under logical consequence. In the AGM framework there are three operations to be considered, namely expansion, contraction and revision.
Meanwhile several variants of this model were proposed. One of which was to represent the beliefs of an agent by a belief base, a set of sentences that is not (necessarily) closed under logical consequence.
Mary-Anne Williams introduced the notion of ensconcement relation on a belief base and introduced two types of contractions: ensconcement-based contractions and brutal contractions.
In this presentation we recall the notion of ensconcement relation and present axiomatic characterizations for these contraction operators.