, Volume 187, Supplement 1, pp 1–42 | Cite as

The dynamics of relevance: adaptive belief revision

  • Frederik Van De PutteEmail author
  • Peter Verdée


This paper presents eight (previously unpublished) adaptive logics for belief revision, each of which define a belief revision operation in the sense of the AGM framework. All these revision operations are shown to satisfy the six basic AGM postulates for belief revision, and Parikh’s axiom of Relevance. Using one of these logics as an example, we show how their proof theory gives a more dynamic flavor to belief revision than existing approaches. It is argued that this turns belief revision (that obeys Relevance) into a more natural undertaking, where analytic steps are performed only as soon as they turn out to be necessary in order to uphold certain beliefs.


Dynamic belief revision Relevance Splittings Adaptive logics 


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  1. Alchourrón C. E., Gärdenfors P., Makinson D. (1985) On the logic of theory change: Partial meet contraction and revision functions. Journal of Symbolic Logic 50: 510–530CrossRefGoogle Scholar
  2. Batens D. (1999) Inconsistency-adaptive logics. In: Orłowska E. (ed) Logic at work. Essays dedicated to the memory of Helena Rasiowa. Physica Verlag (Springer), Heidelberg, pp 445–472Google Scholar
  3. Batens, D. (2001). A general characterization of adaptive logics. Logique et Analyse, 173–175, 45–68. Appeared 2003.Google Scholar
  4. Batens D. (2005) A procedural criterion for final derivability in inconsistency-adaptive logics. Journal of Applied Logic 3: 221–250CrossRefGoogle Scholar
  5. Batens D. (2007) A universal logic approach to adaptive logics. Logica Universalis 1: 221–242CrossRefGoogle Scholar
  6. Batens D., Clercq K., Verdée P., Meheus J. (2009) Yes fellows, most human reasoning is complex. Synthese 166: 113–131CrossRefGoogle Scholar
  7. Batens D., Meheus J., Provijn D., Verhoeven L. (2003) Some adaptive logics for diagnosis. Logic and Logical Philosophy 11/12: 39–65Google Scholar
  8. Batens D., Straßer C., Verdée P. (2009) On the transparency of defeasible logics: Equivalent premise sets, equivalence of their extensions, and maximality of the lower limit. Logique et Analyse 207: 281–304Google Scholar
  9. Bienvenu, M., Herzig, A., & Qi, G. (2008). Prime implicate-based belief revision operators. In Proceedings of the 2008 conference on ECAI 2008: 18th European Conference on Artificial Intelligence (pp. 741–742). Amsterdam: IOS Press.Google Scholar
  10. Chopra S., Parikh R. (2000) Relevance sensitive belief structures. Annals of Mathematics and Artificial Intelligence 28: 259–285CrossRefGoogle Scholar
  11. Gärdenfors P. (1978) Conditionals and changes of belief. Acta Philosophica Fennica 30: 381–404Google Scholar
  12. Gärdenfors P. (1982) Rules for rational changes of belief. Philosophical Studies 34: 88–101Google Scholar
  13. Hansson S. O. (1999) A textbook of belief dynamics. Theory change and database updating. Kluwer, DordrechtCrossRefGoogle Scholar
  14. Hansson, S. O. (2006). The logic of belief revision.
  15. Horsten L. (2007) Welch Philip the undecidability of propositional adaptive logic. Synthese 158: 41–60CrossRefGoogle Scholar
  16. Jackson, P. (1992). Computing prime implicates. In Proceedings of the 1992 ACM annual conference on Communications. CSC ’92 (pp. 65–72). New York: ACM.Google Scholar
  17. Kourousias G., Makinson D. (2006) Respecting relevance in belief change. Análisis Filosófico 26: 53–61Google Scholar
  18. Kourousias G., Makinson D. (2007) Parallel interpolation, splitting, and relevance in belief change. The Journal of Symbolic Logic 72: 994–1002CrossRefGoogle Scholar
  19. Makinson D. (2009) Propositional relevance through letter-sharing. Journal of Applied Logic 7: 377–387CrossRefGoogle Scholar
  20. Parikh R. (1999) Beliefs, belief revision, and splitting languages. Logic, Language, and Computation 2: 266–278Google Scholar
  21. Perrussel, L., Marchi, J., & Zhang, D. (2011). Characterizing relevant belief revision operators. In AI 2010: Advances in Artificial Intelligence. Lecture Notes in Computer Science (Vol. 6464, pp. 42–51). Heidelberg: Springer.Google Scholar
  22. Pollock J. (1987) Defeasible reasoning. Cognitive Science 11(4): 481–518CrossRefGoogle Scholar
  23. Shoham Y. (1987) A semantical approach to nonmonotonic logics. In: Ginsberg M. L. (ed) Readings in non-monotonic reasoning. Morgan Kaufmann, Los Altos, CA, pp 227–249Google Scholar
  24. Stolpe, A. (2010). Relevance, derogation and permission: A case for a normal form for a code of norms. In Lecture Notes in Artificial Intelligence (Lecture Notes in Computer Science) (Vol. 6181, pp. 98–115). Heidelberg: Springer.Google Scholar
  25. Van De Putte F. (2011a) Hierarchic adaptive logics. Logic Journal of IGPL 20(1): 45–72CrossRefGoogle Scholar
  26. Van De Putte, F. (2011b). Prime implicates and relevant belief revision. Journal of Logic and Computation, in press.
  27. Verdée P. (2009) Adaptive logics using the minimal abnormality strategy are \({\Pi^1_1}\) -complex. Synthese 167: 93–104CrossRefGoogle Scholar
  28. Verdée, P. (2012). A proof procedure for adaptive logics. Logic Journal of the IGPL, in press.
  29. Verhoeven L. (2001) All premisses are equal, but some are more equal than others. Logique et Analyse 173–174–175: 165–188Google Scholar
  30. Verhoeven L. (2003) Proof theories for some prioritized consequence relations. Logique et Analyse 183–184: 325–344Google Scholar
  31. Wu M., Zhang M. (2010) Algorithms and application in decision-making for the finest splitting of a set of formulae. Knowledge-Based Systems 23: 70–76CrossRefGoogle Scholar
  32. Wu, M., Zhu, Z., Zhang, M. (2008). Partial meet contraction based on relevance criterion. In Proceedings of the International MultiConference of Engineers and Computer Scientists, Hong Kong.Google Scholar

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© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Centre for Logic and Philosophy of ScienceGhent UniversityGentBelgium

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