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On the Fixpoint Theory of Equality and Its Applications

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Relations and Kleene Algebra in Computer Science (RelMiCS 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4136))

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Abstract

In the current paper we first show that the fixpoint theory of equality is decidable. The motivation behind considering this theory is that second-order quantifier elimination techniques based on a theorem given in [16], when successful, often result in such formulas. This opens many applications, including automated theorem proving, static verification of integrity constraints in databases as well as reasoning with weakest sufficient and strongest necessary conditions.

Supported in part by the grants 3 T11C 023 29 and 4 T11C 042 25 of the Polish Ministry of Science and Information Society Technologies.

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References

  1. Abiteboul, S., Hull, R., Vianu, V.: Foundations of Databases. Addison-Wesley, Reading (1996)

    Google Scholar 

  2. Ackermann, W.: Untersuchungen über das eliminationsproblem der mathematischen logik. Mathematische Annalen 110, 390–413 (1935)

    Article  MathSciNet  Google Scholar 

  3. Barwise, J.: On Moschovakis closure ordinals. Journal of Symbolic Logic 42, 292–296 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  4. Chandra, Harel., D.: Computable queries for relational databases. Journal of Computer and System Sciences 21, 156–178 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  5. Chandra, Harel, D.: Structure and complexity of relational queries. Journal of Com-puter and System Sciences 25, 99–128 (1982)

    Article  MATH  Google Scholar 

  6. Doherty, P., Łukaszewicz, W., Szałas, A.: Computing circumscription revisited. Journal of Automated Reasoning 18(3), 297–336 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  7. Doherty, P., Łukaszewicz, W., Szałas, A.: Computing strongest necessary and weakest sufficient conditions of first-order formulas. In: International Joint Conference on AI (IJCAI’2001), pp. 145–151 (2000)

    Google Scholar 

  8. Immerman, N.: Upper and lower bounds for first-order expressibility. Journal of Computer and System Sciences 25, 76–98 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  9. Kachniarz, J., Szałas, A.: On a static approach to verification of integrity constraints in relational databases. In: Orłowska, E., Szałas, A. (eds.) Relational Methods for Computer Science Applications, pp. 97–109. Springer Physica-Verlag, Heidelberg (2001)

    Google Scholar 

  10. Kolaitis, P., Vardi, M.: On the expressive power of variable-confined logics. In: Proc. IEEE Conf. Logic in Computer Science, pp. 348–359 (1996)

    Google Scholar 

  11. Lifschitz, V.: Circumscription. In: Gabbay, D.M., Hogger, C.J., Robinson, J.A. (eds.) Handbook of Artificial Intelligence and Logic Programming, vol. 3, pp. 297–352. Oxford University Press, Oxford (1991)

    Google Scholar 

  12. Lin, F.: On strongest necessary and weakest sufficient conditions. In: Cohn, A.G., Giunchiglia, F., Selman, B. (eds.) Proc. 7th International Conf. on Principles of Knowl-edge Representation and Reasoning, KR2000, pp. 167–175. Morgan Kaufmann, San Francisco (2000)

    Google Scholar 

  13. Magnusson, M.: DLS* (2005), http://www.ida.liu.se/labs/kplab/projects/dlsstar/

  14. McCarthy, J.: Circumscription: A form of non-monotonic reasoning. Artificial Intelligence Journal 13, 27–39 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  15. Nonnengart, A., Ohlbach, H.J., Szałas, A.: Elimination of predicate quantifiers. In: Ohlbach, H.J., Reyle, U. (eds.) Logic, Language and Reasoning. Essays in Honor of Dov Gabbay, Part I, pp. 159–181. Kluwer, Dordrecht (1999)

    Google Scholar 

  16. Nonnengart, A., Szałas, A.: A fixpoint approach to second-order quantifier elimination with applications to correspondence theory. In: Orłowska, E. (ed.) Logic at Work: Essays Dedicated to the Memory of Helena Rasiowa. Studies in Fuzziness and Soft Computing, vol. 24, pp. 307–328. Springer Physica-Verlag, Heidelberg (1998)

    Google Scholar 

  17. Poizat, B.: Deux ou trois choses que je sais de L n . Journal of Symbolic Logic 47, 641–658 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  18. Szałas, A.: On the correspondence between modal and classical logic: An automated approach. Journal of Logic and Computation 3, 605–620 (1993)

    Article  MathSciNet  MATH  Google Scholar 

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Szałas, A., Tyszkiewicz, J. (2006). On the Fixpoint Theory of Equality and Its Applications. In: Schmidt, R.A. (eds) Relations and Kleene Algebra in Computer Science. RelMiCS 2006. Lecture Notes in Computer Science, vol 4136. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11828563_26

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  • DOI: https://doi.org/10.1007/11828563_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-37873-0

  • Online ISBN: 978-3-540-37874-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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