The correspondence of belief changes in logical settings and the possibilistic framework

Belief change operations in logical settings and the possibilistic framework are reviewed. In logical settings, the Alchourron-Gardenfors-Makinson (AGM) paradigm (1985) and the Katsuno-Mendelzon framework (1992) are reviewed and interdefinability between update and erasure in the AGM paradigm is explained precisely. Moreover, a new identity that captures a relationship from contraction to erasure in the AGM paradigm is introduced and clear relationships among revision, contraction, update and erasure in the AGM paradigm are established. In the possibilistic framework, expansion and above four types of belief change are also formulated, and it is shown that two identities that capture the relationships between update and erasure in the AGM paradigm still remain valid between updating rule and the refined erasing rule