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European Workshop on Logics in Artificial Intelligence

JELIA 1990: Logics in AI pp 267–281Cite as

Systems for knowledge and beliefs

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 478))

Abstract

We investigate a system for knowledge and belief, as introduced in Kraus and Lehmann's [KL]. In [KL] it is observed, that adding the axiom Biφ → BiKiφ to the system gives a collapse of knowledge and belief: (Kiφ ↔ Biφ). We investigate the cause(s) of this problem and suggest a ‘similar’ system that does allow the same axiom without the mentioned collapse. We consider as the main benefit of this paper, however, the techniques that are developed to come to this solution. It appears that applying basic correspondence theory to a multi-modal system allows a systematic examination of possible combinations of epistemic operators.

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References

  1. M. Fattorosi-Barnaba & F. de Caro, Graded Modalities I, in: Studia Logica, 2 (1985), 197–221.

    Google Scholar 

  2. J.F.A.K. van Benthem, Correspondence Theory, in: Handbook of Philosophical Logic, D. Gabbay & F. Guenthner (eds), vol. 2, Reidel, Dordrecht (1984), 167–247.

    Google Scholar 

  3. B.F. Chellas, Modal Logic: An Introduction, Cambridge University Press, Cambridge/London (1980)

    Google Scholar 

  4. R.F. Fagin & J.Y. Halpern, Belief, Awareness, and Limited Reasoning, in: Artificial Intelligence, 34 (1988) 39–76.

    Google Scholar 

  5. G.E. Hughes & M.J. Cresswell, An Introduction to Modal Logic, Methuen & Co. Ltd, London (1977).

    Google Scholar 

  6. Z. Huang & K. Kwast, Awareness, Negation and Logical Omniscience, in Proceedings of JELIA'90, Amsterdam, (1990).

    Google Scholar 

  7. J. Y. Halpern and Y. O. Moses, A Guide to the Modal Logics of Knowledge and Belief, in: Proceedings IJCAI-85, Los Angeles, CA (1985) 480–490

    Google Scholar 

  8. W. van der Hoek & J.-J. Ch. Meyer, Possible Logics for Belief, Report IR-170, Free University Amsterdam (1988).

    Google Scholar 

  9. W. van der Hoek, Systems for Knowledge and Beliefs, Report IR-165, Free University Amsterdam (1989)

    Google Scholar 

  10. W. van der Hoek, Numerieke Modale Logika, paper University of Groningen (1986).

    Google Scholar 

  11. S. Kraus & D. Lehmann, Knowledge, Belief and Time, in: Lecture Notes in Computer Science, L. Kott (ed), 226, ICALP (1986).

    Google Scholar 

  12. H.J. Levesque, A Logic of Implicit and Explicit Belief, in: Proceedings AAAI-84, Austin, TX (1984), 198–202.

    Google Scholar 

  13. F. Voorbraak, The logic of objective knowledge and rational belief, in Proceedings of JELIA'90, Amsterdam (1990).

    Google Scholar 

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Authors and Affiliations

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

    Wiebe van der Hoek

Authors
  1. Wiebe van der Hoek
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J. van Eijck

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© 1991 Springer-Verlag Berlin Heidelberg

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van der Hoek, W. (1991). Systems for knowledge and beliefs. In: van Eijck, J. (eds) Logics in AI. JELIA 1990. Lecture Notes in Computer Science, vol 478. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0018447

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  • DOI: https://doi.org/10.1007/BFb0018447

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53686-4

  • Online ISBN: 978-3-540-46982-7

  • eBook Packages: Springer Book Archive

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