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Awareness, negation and Logical omniscience

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Logics in AI (JELIA 1990)

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

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Abstract

General Epistemic Logics suffer from the problem of logical omniscience, which is that an agent's knowledge and beliefs are closed under implication. There have been many attempts to solve the problem of logical omniscience. However, according to our intuition, sometimes an agent's knowledge and beliefs are indeed closed under implication. Based on the notion of awareness, we introduce two kinds of negations: general negation and strong negation. Moreover, four kinds of implications, general implication, strong implication, weak implication, and semi-strong implication, are introduced to correspond with the two kinds of negations. In our logics of regular awareness, explicit beliefs are not necessarily closed under general implication, which means that agents are not logically omniscient. However, explicit beliefs are closed under strong implication and semi-strong implication, which captures an intuitive closure property of beliefs.

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References

  1. Jon Barwise and John Perry, Situations and Attitudes, MIT Press, 1983.

    Google Scholar 

  2. Johan van Benthem, Modal Logic as a Theory of Information, ITLI LP-89-05, University of Amsterdam, 1989.

    Google Scholar 

  3. Cresswell, M. J., Structured Meanings. MIT Press, 1985.

    Google Scholar 

  4. Dirk van Dalen, Intuitionistic Logic, in:Gabbay, D. M. (ed.) Handbooks of Philosophical Logic, Vol.III, P. Reidel Publishing Company, 1986, 225–339.

    Google Scholar 

  5. C. J. Date, ”Not” is not not, Presentation of Data Base Day, Eindhoven, December, 1989.

    Google Scholar 

  6. Eberle, R. A., The Logic of Believing Knowing, and Inferring. Synthese 26(1974), 356–382.

    Google Scholar 

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

    Google Scholar 

  8. Gabbay, D. M., Semantical Investigations in Heyting's Intuitionistic Logic, S. Reidel Publishing Company, 1981.

    Google Scholar 

  9. Hintikka, J., Knowledge and Belief, Cornell University Press, 1962.

    Google Scholar 

  10. Hintikka, J., Impossible possible worlds vindicated. J. Philosophy 4(1975), 475–484.

    Google Scholar 

  11. W. van der Hoek, J.-J. Ch. Meijer, Possible Logics for Belief, Report IR-170, Vrije University Amsterdam, 1988.

    Google Scholar 

  12. Zhisheng Huang, Dependency of Belief in Distributed Systems, in: Martin Stokhof and Leen Torenvliet (eds.) Proceedings of the 7th Amsterdam Colloquium, (ITLI, University of Amsterdam, 1990) 637–662. Also available: Institute for Language, Logic and Information, Preprint LP-89-09, University of Amsterdam, 1989.

    Google Scholar 

  13. Konolige, K., A deductive model of belief. Proceedings 8th Int. Joint Conf. on AI, 1983, 377–381.

    Google Scholar 

  14. Konolige, K., Belief and incompleteness. in: J. R. Hobbs and R. C. Moore (eds.) Formal Theories of the Commonsense World, Ablex Publishing Company, 1985, 359–404.

    Google Scholar 

  15. Konolige, K., What Awareness Isn't: A Sentential View of Implicit and Explicit Belief, in: J. Y. Halpern (ed.) Theoretical Aspects of Reasoning about Knowledge: Proceedings of the 1986 Conference, (Morgan-Kaufmann, Los Altos, CA, 1986) 241–250.

    Google Scholar 

  16. Lakemeyer, G., Steps towards a First-order logic of Explicit and Implicit Belief, in: J.Y. Halpern (ed.) Theoretical Aspects of Reasoning about Knowledge: Proceedings of the 1986 conference (Morgan-Kaufmann, Los Alots, CA, 1986) 325–340.

    Google Scholar 

  17. Lenzen, W., Recent Work in Epistemic Logic. Acta Phil. Fenn. 30(1978), 1–129.

    Google Scholar 

  18. Levesque, H. J., A logic of implicit and explicit belief, in: Proceedings AAAI-84 Austin, TX (1984) 198–202.

    Google Scholar 

  19. Vardi, M. Y., On epistemic logic and logical omniscience, in: J.Y. Halpern (ed.), Theoretical Aspects of Reasoning about knowledge: Proceedings of the 1986 conference (Morgan-Kaufmann, Los Altos, CA, 1986) 293–306.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Amsterdam, Plantage Muidergracht 24, 1018TV, Amsterdam, The Netherlands

    Zhisheng Huang & Karen Kwast

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  1. Zhisheng Huang
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  2. Karen Kwast
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J. van Eijck

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© 1991 Springer-Verlag Berlin Heidelberg

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Huang, Z., Kwast, K. (1991). Awareness, negation and Logical omniscience. 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/BFb0018448

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  • DOI: https://doi.org/10.1007/BFb0018448

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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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