Journal of Philosophical Logic

, Volume 41, Issue 4, pp 711-733

First online:

A General Family of Preferential Belief Removal Operators

  • Richard BoothAffiliated withUniversity of Luxembourg Email author 
  • , Thomas MeyerAffiliated withCentre for Artificial Intelligence Research, University of KwaZulu-Natal and CSIR Meraka
  • , Chattrakul SombattheeraAffiliated withMahasarakham University

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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. (Artif Intell 174:1339–1368, 2010). However it is not always reasonable to assume completeness of the underlying ordering. In this paper we generalise the structure of Booth et al. (Artif Intell 174:1339–1368, 2010) 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.


Belief revision Belief removal Belief contraction Belief change Plausibility orderings Finite belief bases