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A Note on Graded Modal Logic

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Abstract

We introduce a notion of bisimulation for graded modal logic. Using this notion, the model theory of graded modal logic can be developed in a uniform manner. We illustrate this by establishing the finite model property and proving invariance and definability results.

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References

  1. Van Benthem, J., Exploring Logical Dynamics, Studies in Logic, Language and Information, CSLI Publications, Stanford, 1996.

    Google Scholar 

  2. Cerrato, C., ‘General canonical models for graded normal logics (graded modalities IV)’ Studia Logica 49 (1990), 241-252.

    Google Scholar 

  3. Cerrato, C., ‘Decidability by filtrations for graded normal logics (graded modalities V)’ Studia Logica 53 (1994), 61-74.

    Google Scholar 

  4. Chang, C. C., and H. J. Keisler, Model Theory, North-Holland, Amsterdam, 1973.

    Google Scholar 

  5. De Caro, F., ‘Graded modalities II’ Studia Logica 47 (1988), 1-10.

    Google Scholar 

  6. Donini, F. M., M. Lenzerini, D. Nardi and A. Schaerf, ‘Reasoning in description logics’ in G. Brewka (ed.), Principles of Knowledge Representation, Studies in Logic, Language and Information, CSLI Publications, Stanford, 1996.

    Google Scholar 

  7. Fattorosi-Barnaba, M., and F. De Caro, ‘Graded modalities I’ Studia Logica 44 (1985), 197-221.

    Google Scholar 

  8. Fattorosi-Barnaba, M., and C. Cerrato, ‘Graded modalities III’ Studia Logica 47 (1988), 99-110.

    Google Scholar 

  9. Fine, K., ‘In so many possible worlds’ Notre Dame Journal of Formal Logic 13 (1972), 516-520.

    Google Scholar 

  10. Goble, L. F., ‘Grades of modality’ Logique et Analyse 13 (1970), 323-334.

    Google Scholar 

  11. Van Der Hoek, W., Modalities for Reasoning about Knowledge and Quantities, Phd thesis, Free University of Amsterdam, 1992.

  12. Van Der Hoek, W., ‘On the semantics of graded modalities’ Journal of Applied Non-Classical Logic 2 (1992), 81-123.

    Google Scholar 

  13. Van Der Hoek, W., and M. De Rijke, ‘Generalized quantifiers and modal logic’ Journal of Logic, Language and Information 2 (1993), 19-57.

    Google Scholar 

  14. Van Der Hoek, W., and M. De Rijke, ‘Counting objects’ Journal of Logic and Computation 5 (1995), 325-345.

    Google Scholar 

  15. Kurtonina, N., and M. De Rijke, ‘Bisimulations for temporal logic’ Journal of Logic, Language and Information 6 (1997), 403-425.

    Google Scholar 

  16. Kurtonina, N., and M. De Rijke, ‘Simulating without negation’ Journal of Logic and Computation 7 (1997), 503-524.

    Google Scholar 

  17. Marx, M., Algebraic Relativization and Arrow Logic, PhD thesis, ILLC, University of Amsterdam, 1995.

  18. Nakamura, A., ‘On a logic based on graded modalities’ IECE Trans. Inf. & Syst., E76-D(5) (1992), 527-532.

    Google Scholar 

  19. De Rijke, M., ‘Modal model theory’ Annals of Pure and Applied Logic (to appear).

  20. Schlingloff, H., ‘Expressive completeness of temporal logic of trees’ Journal of Applied Non-Classical Logics 2 (1992), 157-180.

    Google Scholar 

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Authors
  1. Maarten de Rijke
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de Rijke, M. A Note on Graded Modal Logic. Studia Logica 64, 271–283 (2000). https://doi.org/10.1023/A:1005245900406

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