Two axiomatic characterizations for the system of spheres-based (and the Epistemic Entrenchment-based) multiple contractions
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In some recent works (Reis 2011, Fermé and Reis, J. Philos. Log. 41, 29–52, 2012, Fermé and Reis, Rev. Symb. Log. 6, 460–487, 2013) two new kinds of multiple contraction functions have been proposed, namely the system of spheres-based multiple contractions and the epistemic entrenchment-based multiple contractions, as generalizations (to the case of multiple contraction) of the well-known classes of systems of spheres-based and of epistemic entrenchment-based (singleton) contractions. Additionally, a representation theorem for the class of epistemic entrenchment-based multiple contraction has been proposed, and it has been shown that the two newly proposed constructions are equivalent, in the sense that a multiple contraction function is a system of spheres-based multiple contraction if and only if it is an epistemic entrenchment-based multiple contraction. In this paper we present two axiomatic characterizations for those multiple contraction functions which differ from the one mentioned above and, in particular, make use of some more intuitive postulates.
KeywordsBelief change Theory contraction Multiple contraction System of spheres Epistemic entrenchment Axiomatic characterization
Mathematics Subject Classification (2010)03B42 68T27
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- 4.Fuhrmann, A.: Relevant logics, modal logics and theory change. Ph.D. thesis, Australian National University, Camberra (1988)Google Scholar
- 7.Gärdenfors, P., Makinson, D.: Revisions of knowledge systems using epistemic entrenchment. In: Vardi, M.Y. (ed.) Proceedings of the second conference on theoretical aspects of reasoning about knowledge, pp 83–95. Morgan Kaufmann, Los Altos (1988)Google Scholar
- 12.Niederée, R.: Multiple contraction: A further case against Gärdenfors’ principle of recovery. In: Fuhrmann, A., Morreau, M. (eds.) The logic of theory change, pp 322–334. Springer, Berlin (1991)Google Scholar
- 14.Reis, M.D.L.: On theory multiple contraction. Ph.D. thesis, Universidade da Madeira, Funchal (2011). http://hdl.handle.net/10400.13/255