Skip to main content
SpringerLink
Log in

Graded modalities in epistemic logic

  • Conference paper
  • First Online:
Logical Foundations of Computer Science — Tver '92 (LFCS 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 620))

Included in the following conference series:

Abstract

We propose an epistemic logic with so-called graded modalities, in which certain types of knowledge are expressible that are less absolute than in traditional epistemic logic. Beside ‘absolute knowledge’ (which does not allow for any exception), we are also able to express ‘accepting ϕ if there at most n exceptions to ϕ’. This logic may be employed in decision support systems where there are different sources to judge the same proposition. We argue that the logic also provides a link between epistemic logic and the more quantitative (even probabilistic) methods used in AI systems. In this paper we investigate some properties of the logic as well as some applications.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. P. Atzeni and D.S. Parker. Set containment inference and syllogisms. Theoretical Computer Science, 62:39–65, 1988.

    Article  Google Scholar 

  2. M. Fattorosi-Barnaba and C. Cerrato. Graded modalities III. Studia Logica, 47:99–110, 1988.

    Article  Google Scholar 

  3. R.F. Fagin and J.Y. Halpern. Belief, awareness, and limited reasoning. Artificial Intelligence, 34:39–76, 1988.

    Article  Google Scholar 

  4. K. Fine. In so many possible worlds. Notre Dame Journal of Formal Logic, 13:516–520, 1972.

    Google Scholar 

  5. V. Goranko and S. Passy. Using the universal modality: Gains and questions. Preprint, Sofia University, 1990.

    Google Scholar 

  6. G.E. Hughes and M.J. Cresswell. Introduction to Modal Logic. Methuen, London, 1968.

    Google Scholar 

  7. J.Y. Halpern and Y.O. Moses. A guide to the modal logics of knowledge and belief. Proceedings IJCAI-85. Los Angeles, CA, 1985, pages 480–490.

    Google Scholar 

  8. W. van der Hoek, Some Considerations on the Logic PFD, (a Logic Combining modalities and Probabilities), Report Free University IR-227, Amsterdam (1990). To appear in Proc. 2nd Russian Conference on Logic Programming, LNCS (1992).

    Google Scholar 

  9. W. van der Hoek, Qualitative Modalities, proceedings of the Scandinavian Conference on Artificial Intelligence-91, B. Mayoh (ed.) IOS Press, Amsterdam (1991), 322–327.

    Google Scholar 

  10. W. van der Hoek. On the semantics of graded modalities. Technical Report IR-246, Free University of Amsterdam, 1991. To appear in The Journal of Applied Non Classical Logic, vol I, 2 (1992).

    Google Scholar 

  11. W. van der Hoek, Systems for Knowledge and Beliefs, in: In J. van Eijck, editor, Logics in AI-JELIA'90, Lecture Notes in Artificial Intelligence 478, Springer, Berlin, 1991, pp. 267–281. Extended version to appear in Journal of Logic and Computation.

    Google Scholar 

  12. W. van der Hoek, Modalities for Reasoning about Knowledge and Quantities, Ph.D. thesis, Amsterdam, 1992.

    Google Scholar 

  13. W. van der Hoek and J.-J.Ch. Meyer. Possible logics for belief. Technical Report IR-170, Free University of Amsterdam, 1988. To appear in Logique et Analyse.

    Google Scholar 

  14. W. van der Hoek & J.-J.Ch. Meyer, Making Some Issues of Implicit Knowledge Explicit, Report Free University IR-222 (1990). To appear in Foundations of Computer Science.

    Google Scholar 

  15. W. van der Hoek & M. de Rijke, Generalized Quantifiers amd Modal Logic, in: Generalized Quantifiers Theory and Applications, J. van der Does and J. van Eijck (eds), Dutch Network for Logic, Language and Information (1991), pp. 115–142.

    Google Scholar 

  16. W. Lenzen. Glauben, Wissen und Warscheinlichkeit. Springer Verlag, Wien, 1980.

    Google Scholar 

  17. J.-J.Ch. Meyer and W. van der Hoek. Non-monotonic reasoning by monotonic means. In J. van Eijck, editor, Logics in AI-JELIA'90, Lecture Notes in Artificial Intelligence 478, Springer, Berlin, 1991, pages 399–411.

    Google Scholar 

  18. J.-J.Ch. Meyer, W. van der Hoek, and G.A.W. Vreeswijk. Epistemic logic for computer science: A tutorial. EATCS bulletin, 44:242–270, 1991. (Part I), and EATCS bulletin, 45:256–287, 1991. (Part II).

    Google Scholar 

  19. D. Perlis. On the consistency of commonsense reasoning. Computational Intelligence, 2:180–190, 1986.

    Google Scholar 

  20. N. Rescher. Plausible Reasoning, an Introduction to the Theory and Practice of Plausibilistic Inference. Van Gorcum, Assen, 1976.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Computers Science, Free University, Amsterdam, De Boelelaan 1081a, 1081, HV Amsterdam, The Netherlands

    W. van der Hoek & J. -J. Ch. Meyer

  2. University of Nijmegen, Toernooiveld, 6525, ED Nijmegen, The Netherlands

    J. -J. Ch. Meyer

Authors
  1. W. van der Hoek
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. -J. Ch. Meyer
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Anil Nerode Mikhail Taitslin

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

van der Hoek, W., Meyer, J.J.C. (1992). Graded modalities in epistemic logic. In: Nerode, A., Taitslin, M. (eds) Logical Foundations of Computer Science — Tver '92. LFCS 1992. Lecture Notes in Computer Science, vol 620. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023902

Download citation

  • DOI: https://doi.org/10.1007/BFb0023902

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55707-4

  • Online ISBN: 978-3-540-47276-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation