A general family of preferential belief removal operators

Authors:
Richard Booth;Thomas Meyer;Chattrakul Sombattheera
Affiliations:
Mahasarakham University, Faculty of Informatics, Mahasarakham, Thailand;Meraka Institute, CSIR and School of Computer Science, University of Kwazulu-Natal, South Africa;Mahasarakham University, Faculty of Informatics, Mahasarakham, Thailand
Venue:
LORI'09 Proceedings of the 2nd international conference on Logic, rationality and interaction
Year:
2009

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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 [5]. However it is not always reasonable to assume completeness of the underlying ordering. In this paper we generalise the structure of [5] to allow incomparabilities between worlds. We 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.