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Annual Conference on Artificial Intelligence

KI 1997: KI-97: Advances in Artificial Intelligence pp 171–182Cite as

Labelled quantified modal logics

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1303))

Abstract

We present an approach to providing natural deduction style proof systems for a large class of quantified modal logics with varying, increasing, decreasing or constant domains of quantification. The systems we develop are modular both in the behavior of the accessibility relation and quantification relative to the semantics, and in the proofs of soundness and completeness relative to that semantics. Our systems also provide the basis of simple implementations of quantified modal logics in a standard logical framework theorem prover.

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References

  1. Y. Auffray and P. Enjalbert. Modal theorem proving: An equational viewpoint. Journal of Logic and Computation, 2(3):247–297, 1992.

    Google Scholar 

  2. A. Avron. Simple consequence relations. Inf. and Comp., 92:105–139, 1991.

    Google Scholar 

  3. D. Basin, S. Matthews, and L. Viganò. Labelled modal logics: quantifiers. Technical Report MPI-I-97-2-001, MPI für Informatik, Saarbrücken, 1997.

    Google Scholar 

  4. D. Basin, S. Matthews, and L. Viganò. Labelled propositional modal logics: theory and practice. Journal of Logic and Computation, 1997. To appear.

    Google Scholar 

  5. E.Bencivenga, Free logics. In D. Gabbay and F. Guenthner, editors, Handbook of Philosophical Logic, Vol. III, pages 373–426. Reidel, Dordrecht, 1986.

    Google Scholar 

  6. M. Fitting. Proof methods for modal and intuitionistic logics. Kluwer, Dordrecht, 1983.

    Google Scholar 

  7. M. Fitting. Basic modal logic. In D. Gabbay et al., editors, Handbook of Logic in AI and Logic Programming, Vol. I, pages 365–448. Clarendon Press, Oxford, 1993.

    Google Scholar 

  8. D. Gabbay. Labelled deductive systems. Clarendon Press, Oxford, 1996.

    Google Scholar 

  9. J. Carson. Quantification in modal logic. In D. Gabbay and F. Guenthner, editors, Handbook of Philosophical Logic, Vol. II, pages 249–307. Reidel, Dordrecht, 1984.

    Google Scholar 

  10. R. Harper, F. Honsell, and G. Plotkin. A framework for defining logics. Journal of the ACM, 40(1):143–184, 1993.

    Google Scholar 

  11. G. Hughes and M. Cresswell. A new introduction to modal logic. Routledge, 1996.

    Google Scholar 

  12. A. Nerode and R. Shore. Logic for applications. Springer, Berlin, 1993.

    Google Scholar 

  13. H. J. Ohlbach. Semantics based translation methods for modal logics. Journal of Logic and Computation, 1(5):691–746, 1991.

    Google Scholar 

  14. L. C. Paulson. Isabelle: a generic theorem prover. Springer, Berlin, 1994.

    Google Scholar 

  15. J. R. Shoenfield. Mathematical logic. Addison Wesley, Reading, 1967.

    Google Scholar 

  16. D. van Dalen. Logic and structure. Springer, Berlin, 1994.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Institut für Informatik, Universität Freiburg, Am Flughafen 17, D-79110, Freiburg, Germany

    David Basin

  2. Max-Planck-Institut für Informatik, Im Stadtwald, D-66123, Saarbrücken, Germany

    Seán Matthews & Luca Viganò

Authors
  1. David Basin
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  2. Seán Matthews
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  3. Luca Viganò
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Editor information

Gerhard Brewka Christopher Habel Bernhard Nebel

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© 1997 Springer-Verlag Berlin Heidelberg

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Basin, D., Matthews, S., Viganò, L. (1997). Labelled quantified modal logics. In: Brewka, G., Habel, C., Nebel, B. (eds) KI-97: Advances in Artificial Intelligence. KI 1997. Lecture Notes in Computer Science, vol 1303. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3540634932_13

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  • DOI: https://doi.org/10.1007/3540634932_13

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63493-5

  • Online ISBN: 978-3-540-69582-0

  • eBook Packages: Springer Book Archive

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