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Emptiness Relations in Property Systems

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Relational Methods in Computer Science (RelMiCS 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2561))

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Abstract

In this paper, we carry out the modal analysis of emptiness through a modal logic which modalities correspond to emptiness relations in property systems. We mainly address the questions of axiomatization/ completeness and decidability/complexity of our modal logic.

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References

  1. Balbiani, P., Vakarelov, D.: First-order characterization and modal analysis of indiscernibility and complementarity in information systems. In Benferhat, S., Besnard, P. (Editors): Symbolic and Quantitative Approaches to Reasoning with Uncertainty. Springer-Verlag, Lecture Notes in Artificial Intelligence 2143 (2001) 772–781.

    Google Scholar 

  2. Demri, S.: The nondeterministic information logic NIL is PSPACE-complete. Fundamenta Informaticæ42 (2000) 211–234.

    MATH  MathSciNet  Google Scholar 

  3. Demri, S., Orłowska, E., Vakarelov, D.: Indiscernibility and complementarity relations in information systems. In Gerbrandy, J., Marx, M., de Rijke, M., Venema, Y. (Editors): JFAK: Essays Dedicated to Johan van Benthem on the Occasion of his 50th Birthday. Amsterdam University Press (1999) http://turing.wins.uva.nl/~j50/cdrom/contribs/demri/index.html.

  4. Hughes, G., Cresswell, M.: A Companion to Modal Logic. Methuen (1984).

    Google Scholar 

  5. Ladner, R.: The computational complexity of provability in systems of modal propositional logic. SIAM Journal on Computing 6 (1977) 467–480.

    Article  MATH  MathSciNet  Google Scholar 

  6. Orłowska, E.: Logic of nondeterministic information. Studia Logica 44 (1985) 91–100.

    Article  MATH  MathSciNet  Google Scholar 

  7. Orłowska, E.: Kripke semantics for knowledge representation logics. Studia Logica 49 (1990) 255–272.

    Article  MATH  MathSciNet  Google Scholar 

  8. Orłowska, E. (Editor): Incomplete Information: Rough Set Analysis. Physica-Verlag, Studies in Fuzziness and Soft Computing 13 (1998).

    Google Scholar 

  9. Orłowska, E., Pawlak, Z.: Representation of nondeterministic information. Theoretical Computer Science 29 (1984) 27–39.

    Article  MathSciNet  Google Scholar 

  10. Pawlak, Z.: Information systems — theoretical foundations. Information Systems 6 (1981) 205–218.

    Article  MATH  Google Scholar 

  11. Savitch, W.: Relationships between nondeterministic and deterministic tape complexities. Journal of Computer and System Sciences 4 (1970) 177–192.

    MATH  MathSciNet  Google Scholar 

  12. Spaan, E.: The complexity of propositional tense logics. In de Rijke, M. (Editor): Diamonds and Defaults: Studies in Pure and Applied Intensional Logic. Kluwer, Synthese Library 229 (1993) 287–307.

    Google Scholar 

  13. Vakarelov, D.: A modal logic for similarity relations in Pawlak knowledge representation systems. Fundamenta Informaticæ15 (1991) 61–79.

    MATH  MathSciNet  Google Scholar 

  14. Vakarelov, D.: Modal logics for knowledge representation systems. Theoretical Computer Science 90 (1991) 433–456.

    MATH  MathSciNet  Google Scholar 

  15. Vakarelov, D.: A duality between Pawlak’s knowledge representation systems and BI-consequence systems. Studia Logica 55 (1995) 205–228.

    Article  MATH  MathSciNet  Google Scholar 

  16. Vakarelov, D.: Information systems, similarity relations and modal logics. In Orłowska, E. (Editor): Incomplete Information: Rough Set Analysis. Physica-Verlag, Studies in Fuzziness and Soft Computing 13 (1998) 492–550.

    Google Scholar 

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© 2002 Springer-Verlag Berlin Heidelberg

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Balbiani, P. (2002). Emptiness Relations in Property Systems. In: de Swart, H.C.M. (eds) Relational Methods in Computer Science. RelMiCS 2001. Lecture Notes in Computer Science, vol 2561. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36280-0_2

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  • DOI: https://doi.org/10.1007/3-540-36280-0_2

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00315-1

  • Online ISBN: 978-3-540-36280-7

  • eBook Packages: Springer Book Archive

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