Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-24T23:14:05.792Z Has data issue: false hasContentIssue false
  • English
  • Français

Logics of belief change without linearity

Published online by Cambridge University Press:  12 March 2014

John Cantwell
John Cantwell*
Affiliation:
Department of Philosophy, Uppsala University, Drottninggatan 4, 75236 Uppsala, Sweden, E-mail:[email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Ever since [4]. systems of spheres have been considered to give an intuitive and elegant way to give a semantics for logics of theory- or belief- change. Several authors [5, 11] have considered giving up the rather strong assumption that systems of spheres be linearly ordered by inclusion. These more general structures are called hypertheories after [8]. It is shown that none of the proposed logics induced by these weaker structures are compact and thus cannot be given a strongly complete axiomatization in a finitary logic. Complete infinitary axiomatizations are given for several intuitive logics based on hypertheories that are not linearly ordered by inclusion.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 65 , Issue 4 , December 2000 , pp. 1556 - 1575
Copyright
Copyright © Association for Symbolic Logic 2000

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Alchourrón, C., Gärdenfors, P., and Makinson, D., On the logic of theory change: Partial meet functions for contraction and revision, this Journal, vol. 50 (1985), pp. 510–530.Google Scholar
[2]Cantwell, J., Some logics of iterated revision, Studia Logica, vol. 63 (1999), pp. 49–84.CrossRefGoogle Scholar
[3]Gärdenfors, P. and Makinson, D., Revisions of knowledge systems using epistemic entrenchment, Theoretical aspects of reasoning about knowledge (Vardi, M., editor), Morgan Kaufman, Los Altos, CA, 1988, pp. 83–95.Google Scholar
[4]Grove, A., Two modelings for theory change, Journal of Philosophical Logic, vol. 17 (1988), pp. 157–170.CrossRefGoogle Scholar
[5]Lindström, S. and Rabinowicz, W., Epistemic entrenchment with incomparabilities and relational belief revision. The logic of theory change (Fuhrmann, A. and Morreau, M., editors), Springer-Verlag, Berlin, 1991, pp. 93–126.CrossRefGoogle Scholar
[6]Rott, H., Preferential belief change using generalized epistemic entrenchment, Journal of Logic, Language and Information, vol. 1 (1992), pp. 45–78.CrossRefGoogle Scholar
[7]Segerberg, K., A model existence theorem in infinitary propositional modal logic, Journal of Philosophical Logic, vol. 21 (1994), pp. 337–367.CrossRefGoogle Scholar
[8]Segerberg, K., Belief revision from the point of view ofdoxastic logic, Bulletin of the IGPL, vol. 3 (1995a), pp. 535–553.CrossRefGoogle Scholar
[9]Segerberg, K., Some questions about hypertheories, Logic for a change (Hansson, S.O. and Rabinowicz, W., editors), Uppsala Prints and Preprints in Philosophy, Uppsala, 1995b.Google Scholar
[10]Segerberg, K., Three recipes for revision, Uppsala Prints and Preprints in Philosophy, no. 11, Uppsala University, The department of philosophy, 1996.CrossRefGoogle Scholar
[11]Segerberg, K., Proposal for a theory of belief revision along the lines of Lindström and Rabinowicz, 1997, In press.CrossRefGoogle Scholar