Belief Liberation (and Retraction)
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
We provide a formal study of belief retraction operators that do not necessarily satisfy the (Inclusion) postulate. Our intuition is that a rational description of belief change must do justice to cases in which dropping a belief can lead to the inclusion, or ‘liberation’, of others in an agent's corpus. We provide two models of liberation via retraction operators: ρ-liberation and linear liberation. We show that the class of ρ-liberation operators is included in the class of linear ones and provide axiomatic characterisations for each class. We show how any retraction operator (including the liberation operators) can be ‘converted’ into either a withdrawal operator (i.e., satisfying (Inclusion)) or a revision operator via (a slight variant of) the Harper Identity and the Levi Identity respectively.
- ALCHOURRÓN, C., P. GÄRDENFORS, and D. MAKINSON, ‘On the logic of theory change: Partial meet contraction and revision functions’, Journal of Symbolic Logic, 50:510–530, 1985.
- BOCHMAN, A., ‘Belief contraction as nonmonotonic inference’, Journal of Symbolic Logic, 65:605–626, 2000.
- CHOPRA, S., K. GEORGATOS, and R. PARIKH, ‘Relevance sensitive non-monotonic inference for belief sequences’, Journal of Applied Non-Classical Logics, 11(1-2):131–150, 2001.
- CHOPRA, S., A. GHOSE, and T. MEYER, ‘Non-prioritized ranked belief change’, Journal of Philosophical Logic, 32(4):417–443, 2003. CrossRef
- DOYLE, J., ‘Reason maintenance and belief revision: Foundations versus coherence theories’, in P. GÄrdenfors, (ed.), Belief Revision, Cambridge University Press, 1992, pp. 29–51.
- FREUND, M., ‘On rational preferences’, Journal of Mathematical Economics, 30:215–228, 1998. CrossRef
- FUHRMANN, A., and S.O. HANSSON, ‘A survey of multiple contractions’, Journal of Logic, Language and Information, 3:39–76, 1994.
- GÄRDENFORS, P., Knowledge in Flux, MIT Press, 1988.
- GLAISTER, S.M., ‘Recovery recovered’, Journal of Philosophical Logic, 29:171–206, 2000. CrossRef
- HANSSON, S. O., ‘Theory contraction and base contraction uni.ed’, Journal of Symbolic Logic, 58:602–625, 1993.
- HANSSON, S. O., A Textbook of Belief Dynamics, Kluwer Academic Publishers, 1999.
- LEHMANN, D., ‘Belief revision, revised’, in Proceedings of the Fourteenth International Joint Conference on Artificial Intelligence (IJCAI'95), 1995, pp. 1534–1540.
- MAKINSON, D., ‘On the status of the postulate of recovery in the logic of theory change’, Journal of Philosophical Logic, 16:383–394, 1987. CrossRef
- MEYER, T., J. HEIDEMA, W. LABUSCHAGNE, and L. LEENEN, ‘Systematic withdrawal’, Journal of Philosophical Logic, 31(5):415–443, 2002. CrossRef
- NEBEL, B., ‘How hard is it to revise a belief base?’, in D. Dubois and H. Prade, (eds.), Handbook of Defeasible Reasoning and Uncertainty Management Systems, Vol. 3: Belief Change, Kluwer Academic Publishers, 1998, pp. 77–145.
- REITER, R., ‘A logic for default reasoning’, Artificial Intelligence, 13:81–132, 1980. CrossRef
- ROTT, H., and M. PAGNUCCO, ‘Severe withdrawal (and recovery)’, Journal of Philosophical Logic, 28:501–547, 1999. CrossRef
- Belief Liberation (and Retraction)
Volume 79, Issue 1 , pp 47-72
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
- Additional Links
- Belief revision
- AGM theory
- Inclusion postulate