General family of preferential belief removal operators - [Workshop on LORI-II]

Abstract

Most belief change operators in the AGM tradition assume an underlying plausibility ordering over the possible worlds which is transitive and complete. A unifying structure for these operators, based on supplementing the plausibility ordering with a second, guiding, relation over the worlds was presented in [Booth et al., 2004]. However it is not always reasonable to assume completeness of the underlying ordering. In this paper the authors generalise the structure of [Booth et al., 2004] to allow incomparabilities between worlds. The authors axiomatise the resulting class of belief removal functions, and show that it includes an important family of removal functions based on finite prioritised belief bases. The authors also look at some alternative notions of epistemic entrenchment which become distinguishable once the authors allow incomparabilities.