Logics of Belief over Weighted Structures

  • Minghui Ma
  • Meiyun Guo
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6953)


We explore logics of belief over weighted structures under the supposition that everything believed by an agent has a weight in the range of agent’s belief. We first define static graded belief logics which are complete with respect to the class of all weighted frames. Furthermore, we discuss their public announcement and dynamic epistemic extensions. We may also define notions of plausible belief by comparing weights of formulas at the current state in a weighted model. This approach is not a new one but we provide new logics and their dynamic extensions which can capture some intuitive notions of belief and their dynamics.


Modal Logic Belief Revision Weighted Model Epistemic Logic Weighted Structure 
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  1. 1.
    Alchourròn, C., Gärdenfors, P., Makinson, D.: On the logic of theory change: Partial meet contraction and revision functions. Journal of Symbolic Logic 50, 510–530 (1985)Google Scholar
  2. 2.
    Aucher, G.: A Combined System for Update Logic and Belief Revision. Master’s thesis, University of Amsterdam, The Netherlands (2004)Google Scholar
  3. 3.
    Baltag, A., Moss, L., Solecki, S.: The logic of public announcements: Common knowledge and private suspicions. In: TARK, pp. 43–56 (1998)Google Scholar
  4. 4.
    van Benthem, J.: Logical Dynamics and Information Flow (2010) (manuscript)Google Scholar
  5. 5.
    van Benthem, J.: Modal Logic for Open Minds. CSLI Publications, Stanford (2010)Google Scholar
  6. 6.
    van Benthem, J., Gerbrandy, J., Kooi, B.: Dynamic update with probabilities. Studia Logica 93, 67–96 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge Univeristy Press, Cambridge (2001)Google Scholar
  8. 8.
    Burgess, J.: Quick completeness proofs for some logics of conditionals. Notre Dame Journal of Formal Logic 22, 76–84 (1981)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    de Caro, F.: Graded modalities ii (canonical models). Studia Logica 47, 1–10 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Chellas, B.: Modal Logic: an introduction. Cambridge University Press, Cambridge (1980)CrossRefzbMATHGoogle Scholar
  11. 11.
    D’Agostino, Visser, A.: Finality regained: a coalgebraic study of scott-sets and multisets. Archive for Mathematical Logic 41, 267–298 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Fagin, R., Halpern, J.: Reasoning about knowledge and probability. Journal of the ACM 41, 340–367 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Fattorosi-Barnaba, M., de Caro, F.: Graded modalities i. Studia Logica 44, 197–221 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Fine, K.: In so many possible worlds. Notre Dame Journal of Formal Logic 13, 516–520 (1972)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Herzig, A., Longin, D.: On modal probability and belief. In: Nielsen, T.D., Zhang, N.L. (eds.) ECSQARU 2003. LNCS (LNAI), vol. 2711, pp. 62–73. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  16. 16.
    Hintikka, J.: Knowledge and Belief. Cornell University Press, Ithica (1962)Google Scholar
  17. 17.
    van der Hoek, W., Meyer, J.J.: Graded modalities in epistemic logic. In: Logical Foundations of Computer Science-Tver 1992, pp. 503–514 (1992)Google Scholar
  18. 18.
    Kooi, B.: Probabilistic dynamic epistemic logic. Journal of Logic, Language and Information 12, 381–408 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    van Ditmarsch, H., van der Hoek, W., Kooi, B.: Dynamic Epistemic Logic. Springer, Heidelberg (2007)CrossRefzbMATHGoogle Scholar
  20. 20.
    Kurzen, L., Velázquez-Quesada, F. (eds.): Logics for dynamics of information and preferences, seminar’s yearbook 2008, pp. 208–219. Institute for Logic, Language and Computation (2008)Google Scholar
  21. 21.
    Ma, M.: Model Theory for Graded Modal Lnaguages. Ph.D. thesis, Tsinghua University, Beijing (2011)Google Scholar
  22. 22.
    Meyer, J.J., van der Hoek, W.: Epistemic Logic for AI and Computer Science. Cambridge University Press, Cambridge (1995)CrossRefzbMATHGoogle Scholar
  23. 23.
    Plaza, J.: Logics of public communications. In: Proceedings of the 4th International Symposium on Methodologies for Intelligent Systems, pp. 201–216 (1989)Google Scholar
  24. 24.
    de Rijke, M.: A note on graded modal logic. Studia Logica 64, 271–283 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Veltman, F.: Logics for Conditionals. Ph.D. thesis, University of Amsterdam, The Netherlands (2011)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Minghui Ma
    • 1
  • Meiyun Guo
    • 1
  1. 1.Institute of Logic and IntelligenceSouthwest UniversityBeibeiChina

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