Journal of Logic, Language and Information

, Volume 8, Issue 4, pp 429–443 | Cite as

A Power Algebra for Theory Change

  • K. Britz


Various representation results have been established for logics of belief revision, in terms of remainder sets, epistemic entrenchment, systems of spheres and so on. In this paper I present another representation for logics of belief revision, as an algebra of theories. I show that an algebra of theories, enriched with a set of rejection operations, provides a suitable algebraic framework to characterize the theory change operations of systems of belief revision. The theory change operations arise as power operations of the conjunction and disjunction connectives of the underlying logic.

belief contraction belief revision power orders theory change 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Alchourrón, C.E. and Makinson, D., 1981, “New studies in deontic logic,” pp. 125–148 in New Studies in Deontic Logic, R. Hilpinen, ed., Dordrecht: Reidel.Google Scholar
  2. Alchourrón, C.E., Gärdenfors, P., and Makinson, D., 1985, “On the logic of theory change: Partial meet functions for contraction and revision,” Journal of Symbolic Logic 50, 510–530.Google Scholar
  3. Brink, C. and Heidema, J., 1989, “A verisimilar ordering of propositional theories: The infinite case,” Technical Report, TR-ARP-1/89, Research School of Social Sciences, Australian National University.Google Scholar
  4. Brink, C. and Rewitzky, I., 1999, Power Structures and Program Semantics, Studies in Logic, Language and Information, Stanford, CA: CLSI.Google Scholar
  5. Fuhrmann, A. and Hansson, S.O., 1994, “A survey of multiple contractions,” Journal of Logic, Language, and Information 3, 39–76.Google Scholar
  6. Gärdenfors, P., 1984, “Epistemic importance and minimal changes of belief,” Australasian Journal of Philosophy 62, 136–157.Google Scholar
  7. Gärdenfors, P., 1988, Knowledge in Flux: Modelling the Dynamics of Epistemic States, Cambridge, MA: MIT Press.Google Scholar
  8. Gärdenfors, P. and Makinson, D., 1988, “Revisions of knowledge systems using epistemic entrenchment,” pp. 83–95 in Proceedings of the Second Conference on Theoretical Aspects of Reasoning about Knowledge, M. Vardi, ed., Los Altos, CA: Morgan Kaufmann.Google Scholar
  9. Grove, A., 1988, “Two modellings for theory change,” Journal of Philosophical Logic 17, 157–170.Google Scholar
  10. Hansson, S.O., 1989, “New operators for theory change,” Theoria 55, 114–132.Google Scholar
  11. Katsuno, H. and Mendelzon, A.O., 1991, “Knowledge base revision and minimal change,” Artificial Intelligence 52, 263–294.Google Scholar
  12. Katsuno, H. and Mendelzon, A.O., 1992, “On the difference between updating a knowledge base and revising it,” pp. 183–203 in Belief Revision, P. Gärdenfors, ed., Cambridge: Cambridge University Press.Google Scholar
  13. Tarski, A., 1956, “Foundations of the calculus of systems,” pp. 342–383 in Logic, Semantics, Metamathematics: Papers from 1923 to 1938, A. Tarski, ed., J.H. Woodger, trans., London: Oxford University Press.Google Scholar

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • K. Britz
    • 1
  1. 1.Department of Computer ScienceUniversity of South AfricaPretoriaSouth Africa

Personalised recommendations