Advertisement

Two axiomatic characterizations for the system of spheres-based (and the Epistemic Entrenchment-based) multiple contractions

  • Maurício D. L. ReisEmail author
  • Pavlos Peppas
  • Eduardo Fermé
Article

Abstract

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.

Keywords

Belief change Theory contraction Multiple contraction System of spheres Epistemic entrenchment Axiomatic characterization 

Mathematics Subject Classification (2010)

03B42 68T27 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alchourrón, C., Gärdenfors, P., Makinson, D.: On the logic of theory change: partial meet contraction and revision functions. J. Symb. Log. 50, 510–530 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Fermé, E., Reis, M.D.L.: System of spheres-based multiple contractions. J. Philos. Log. 41, 29–52 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Fermé, E., Reis, M.D.L.: Epistemic entrenchment-based multiple contractions. Rev. Symb. Log. 6, 460–487 (2013). doi: 10.1017/S1755020313000105 MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Fuhrmann, A.: Relevant logics, modal logics and theory change. Ph.D. thesis, Australian National University, Camberra (1988)Google Scholar
  5. 5.
    Fuhrmann, A., Hansson, S.O.: A survey of multiple contraction. J. Log. Lang. Inf. 3, 39–74 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Gärdenfors, P.: Knowledge in flux: modeling the dynamics of epistemic states. MIT Press, Cambridge (1988)zbMATHGoogle Scholar
  7. 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
  8. 8.
    Grove, A.: Two modellings for theory change. J. Philos. Log. 17, 157–170 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Hansson, S.O.: New operators for theory change. Theoria 55, 114–132 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Hansson, S.O.: A textbook of belief dynamics. Theory change and database updating, applied logic series, vol. 11. Kluwer Academic Publishers, Dordrecht (1999)zbMATHGoogle Scholar
  11. 11.
    Hansson, S.O.: Decomposition of multiple AGM contraction: possibility and impossibility results. Log. J. IGPL 22(4), 696–710 (2014). doi: 10.1093/jigpal/jzu014 MathSciNetCrossRefzbMATHGoogle Scholar
  12. 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
  13. 13.
    Peppas, P., Williams, M.A.: Constructive modelings for theory change. Notre Dame Journal of Formal Logic 36(1), 120–133 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Reis, M.D.L.: On theory multiple contraction. Ph.D. thesis, Universidade da Madeira, Funchal (2011). http://hdl.handle.net/10400.13/255
  15. 15.
    Reis, M.D.L.: On the interrelation between systems of spheres and epistemic entrenchment relations. Log. J. IGPL 22(1), 126–146 (2014). doi: 10.1093/jigpal/jzt037 MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Maurício D. L. Reis
    • 1
    • 2
    Email author
  • Pavlos Peppas
    • 3
    • 4
  • Eduardo Fermé
    • 1
    • 2
  1. 1.Universidade da MadeiraFunchalPortugal
  2. 2.NOVA Laboratory for Computer Science and Informatics (NOVA LINCS)Universidade Nova de LisboaLisboaPortugal
  3. 3.Department of Business AdministrationUniversity of PatrasPatrasGreece
  4. 4.QCIS, Faculty of Engineering and ITUniversity of TechnologySydneyAustralia

Personalised recommendations