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On the semantics of the unknown

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Practical Reasoning (FAPR 1996)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1085))

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Abstract

How can a database express and conclude that it has information on some sentence Φ but not on Ψ? We develop a formal semantics for an operator □, to be read as “It is entailed by the database that ... ”. We define a consequence relation based on a preference semantics and analyze under which circumstances this relation fulfils the condition that ¬□Φ is entailed by a set X of formulas whenever □ ∉ Cn(X). It turns out that this condition holds if the elements of X are modal Horn clauses or propositional sentences. We further relate our logic to some well known nonmonotonic logics. We show that it is located between autoepistemic logic and McDermott's nonmonotonic S5; moreover, all S5 theorems are valid. But unlike McDermott's nonmonotonic S5 it does not collapse to the monotonic case.

The author would like to thank Gerd Brewka and Joachim Hertzberg for invaluable comments on a draft version of this paper.

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References

  1. P. Brazdil and K. Konolige (Editors) Machine Learning, Meta-Reasoning and Logics, Kluwer, Norwell, 1990.

    Google Scholar 

  2. Brian F. Chellas Modal Logic, Cambridge University Press, Cambridge, 1980.

    Google Scholar 

  3. Werner Emde Modellbildung, Wissensrevision und Wissensrepräsentation im maschinellen Lernen, Springer, Berlin, 1991.

    Google Scholar 

  4. J. Doyle and D. McDermott Nonmonotonic Logic I, Artificial Intelligence, Vol.13, 1980.

    Google Scholar 

  5. H. Hirsh Overgenerality in EBG, in Machine Learning, Meta-Reasoning and Logics edited by Brazdil and Konolige, Kluwer, Norwell, 1990.

    Google Scholar 

  6. Hughes and Cresswell Introduction to modal logic, Routledge, London, 1990.

    Google Scholar 

  7. Kurt Konolige On the Relation between Default and Autoepistemic Logic, Artificial Intelligence, Vol.35, 1988.

    Google Scholar 

  8. Kraus, Lehmann and Magidor Nonmonotonic Reasoning, Preferential models and Cumulative Logics, Artificial Intelligence, Vol.44, 1990.

    Google Scholar 

  9. W.Lukaszewicz Non-Monotonic Reasoning, Ellis Horwood Ltd., Chichester, 1990.

    Google Scholar 

  10. D. McDermott Nonmonotonic Logic II, Journal of the ACM, Vol.29, 1982.

    Google Scholar 

  11. R. Moore Semantical considerations on Nonmonotonic Logic, Artificial Intelligence, Vol.25, 1985.

    Google Scholar 

  12. K. Morik, S. Wrobel, J. Kietz and W. Emde Knowledge Acquisition and Machine Learning, Academic Press, London, 1933.

    Google Scholar 

  13. R. Reiter A Logic for Default Reasoning, Artificial Intelligence, Vol.13, 1980.

    Google Scholar 

  14. Y. Shoham Reasoning about change, MIT Press, Cambridge MA, 1988.

    Google Scholar 

  15. Robert C. Stalnaker A Note on Nonmonotonic Modal Logic, Artificial Intelligence, Vol.64 1993.

    Google Scholar 

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Dov M. Gabbay Hans Jürgen Ohlbach

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© 1996 Springer-Verlag Berlin Heidelberg

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Weber, S. (1996). On the semantics of the unknown. In: Gabbay, D.M., Ohlbach, H.J. (eds) Practical Reasoning. FAPR 1996. Lecture Notes in Computer Science, vol 1085. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61313-7_105

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  • DOI: https://doi.org/10.1007/3-540-61313-7_105

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61313-8

  • Online ISBN: 978-3-540-68454-1

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