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Real Algebraic Geometry and Constraint Databases

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Handbook of Spatial Logics

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References

  • Afrati, F., Cosmadakis, S., Grumbach, S., and Kuper, G. (1994). Linear versus polynomial constraints in database query languages. In Borning, A., editor, Proceedings of the 2nd Workshop on Principles and Practice of Constraint Programming, volume 874 of Lecture Notes in Computer Science, pages 181–192, Berlin. Springer-Verlag.

    Google Scholar 

  • Andradas, C., Bröcker, L., and Ruiz, J. M. (1996). Constructible sets in real geometry, volume 33 of Ergebnisse der Mathematik und ihrer Grenzgebiete. Springer-Verlag.

    Google Scholar 

  • Basu, S., Pollack, R., and Roy, M.-F. (2003a). Algorithms in real algebraic geometry, volume 10 of Algorithms and Computation in Mathematics. Springer-Verlag.

    Google Scholar 

  • Basu, S., Pollack, R., and Roy, M.-F. (2003b). Algorithms in Real Algebraic Geometry, volume 10 of Algorithms and Computation in Mathematics. Springer-Verlag.

    Google Scholar 

  • Belegradek, O. V., Stolboushkin, A. P., and Taitslin, M. A. (1996). On order-generic queries. Technical Report 96-01, DIMACS.

    Google Scholar 

  • Benedetti, R. and Risler, J.-J. (1990). Real algebraic and semi-algebraic sets. Actualités Mathématiques. [Current Mathematical Topics]. Hermann.

    Google Scholar 

  • Benedikt, M., Dong, G., Libkin, L., and Wong, L. (1996). Relational expressive power of constraint query languages. In Proceedings of the 15th ACM Symposium on Principles of Database Systems, pages 5–16.

    Google Scholar 

  • Benedikt, M., Grohe, M., Libkin, L., and Segoufin, L. (2003). Reachability and connectivity queries in constraint databases. J. Comput. System Sci., 66(1):169–206.

    Article  Google Scholar 

  • Benedikt, M. and Keisler, H. J. (2000). Definability over linear constraints. In Clote, P. and Schwichtenberg, H., editors, Proceedings of Computer Science Logic, 14th Annual Conference of the EACSL, volume 1862 of Lecture Notes in Computer Science, pages 217–231. Springer-Verlag.

    Google Scholar 

  • Benedikt, M., Kuijpers, B., Löding, C, Van den Bussche, J., and Wilke, T. (2006). A characterization of first-order topological properties of planar spatial data. Journal of the ACM.

    Google Scholar 

  • Benedikt, M. and Libkin, L. (1996). On the structure of queries in constraint query languages. In 11th Annual IEEE Symposium on Logic in Computer Science, pages 25–34.

    Google Scholar 

  • Benedikt, M. and Libkin, L. (2000). Safe constraint queries. SIAM J. Comput., 29(5):1652–1682.

    Article  Google Scholar 

  • Benedikt, M.A. and Libkin, L. (1997). Languages for relational databases over interpreted structures. In Proceedings of the 16th ACM Symposium on Principles of Database Systems, pages 87–98.

    Google Scholar 

  • Bochnak, J., Coste, M., and Roy, M.-F. (1987). Géométrie algébrique réelle. Springer-Verlag.

    Google Scholar 

  • Bochnak, J., Coste, M., and Roy, M.-F. (1998). Real algebraic geometry, volume 36 of Ergebnisse der Mathematik und ihrer Grenzgebiete. Springer-Verlag.

    Google Scholar 

  • Caviness, B.F. and Johnson, J.R. (1998). Quantifier Elimination and Cylindrical Algebraic Decomposition. New York: Springer-Verlag.

    Google Scholar 

  • Codd, E. (1970). A relational model for large shared databanks. Communications of the ACM, 13(6):377–387.

    Article  Google Scholar 

  • Collins, G.E. (1975). Quantifier elimination for real closed fields by cylindrical algebraic decomposition. In Brakhage, H., editor, Automata Theory and Formal Languages, volume 33 of Lecture Notes in Computer Science, pages 134–183, Berlin. Springer-Verlag.

    Google Scholar 

  • Coste, M (2000a). An Introduction to O-minimal Geometry. Istituti Editoriali e Poligrafici Internazionali, Pisa.

    Google Scholar 

  • Coste, M (2000b). An Introduction to Semialgebraic Geometry. Istituti Editoriali e Poligrafici Internazionali, Pisa.

    Google Scholar 

  • Ebbinghaus, H.-D. and Flum, J. (1995). Finite model theory. Perspectives in Mathematical Logic. Springer-Verlag.

    Google Scholar 

  • Ebbinghaus, H.-D., Flum, J., and Thomas, W. (1984). Mathematical Logic. Undergraduate Texts in Mathematics. Springer-Verlag.

    Google Scholar 

  • Geerts, F. (2003). Expressing the box cone radius in the relational calculus with real polynomial constraints. Discrete Comput. Geom., 30(4):607–622.

    Google Scholar 

  • Geerts, F. and Kuijpers, B. (2000). Linear approximation of planar spatial databases using transitive-closure logic. In Proceedings of the 19th ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems, pages 126–135.

    Google Scholar 

  • Geerts, F. and Kuijpers, B. (2005). On the decidability of termination of query evaluation in transitive-closure logics for polynomial constraint databases. Theoretical Computer Science, 336(1):125–151. Database Theory–Special issue with selected papers of ICDT’03.

    Article  Google Scholar 

  • Giusti, M., Lecerf, G., and Salvy, B. (2001). A Gröbner free alternative for polynomial system solving. Journal of Complexity, 17(1):154–211.

    Article  Google Scholar 

  • Grohe, M. and Segoufin, L. (2002). On first-order topological queries. ACM Transactions on Computational Logic, 3(3):336–358.

    Article  Google Scholar 

  • Grumbach, S. and Su, J. (1995). First-order definability over constraint databases. In Proceedings of 1st Conference on Principles and Practice of Constraint Programming, volume 976 of Lecture Notes in Computer Science. Springer-Verlag.

    Google Scholar 

  • Grumbach, S., Su, J., and Tollu, C. (1995). Linear constraint query languages: expressive power and complexity. In Leivant, D., editor, Logic and Computational Complexity, volume 960 of Lecture Notes in Computer Science, pages 426–446. Springer-Verlag.

    Google Scholar 

  • Gyssens, M., Van den Bussche, J., and Van Gucht, D. (1999). Complete geometric query languages. J. Comput. System Sci., 58(3):483–511.

    Article  Google Scholar 

  • Heintz, J., Roy, M.-F., and Solernó, P. (1993). Description of the connected components of a semialgebraic set in single exponential time. Discrete and Computational Geometry, 6:1–20.

    Google Scholar 

  • Hong, H. (1990). QEPCAD - quantifier elimination by partial cylindrical algebraic decomposition. http://www.cs.usna.edu/~qepcad/B/QEPCAD.html.

  • Kanellakis, P. C., Kuper, G., and Revesz, P. Z. (1995). Constraint query languages. Journal of Computer and System Sciences, 51:26–52.

    Article  Google Scholar 

  • Kreutzer, S. (2001). Operational semantics for fixed-point logics on constraint databases. In Logic for programming, artificial intelligence, and reasoning, volume 2250 of Lecture Notes in Compututer Science, pages 470–484. Springer-Verlag.

    Google Scholar 

  • Kuijpers, B., Paredaens, J., and Van den Bussche, J. (2000). Topological elementary equivalence of closed semi-algebraic sets in the real plane. J. Symbolic Logic, 65(4):1530–1555.

    Article  Google Scholar 

  • Kuper, G. M., Libkin, L., and Paredaens, J., editors (2000). Constraint Databases. Springer-Verlag.

    Google Scholar 

  • Motzkin, T. S. (1936). Beiträge zur Theorie der linearen Ungleichungen. Doctoral dissertation. Universität Zürich.

    Google Scholar 

  • Paredaens, J., Van den Bussche, J., and Van Gucht, D. (1994). Towards a theory of spatial database queries. In Proceedings of the Thirteenth ACM Symposium on Principles of Database Systems, pages 279–288.

    Google Scholar 

  • Paredaens, J., Van den Bussche, J., and Van Gucht, D. (1995). First-order queries on finite structures over the reals. In Proceedings of the 10th IEEE Symposium on Logic in Computer Science, pages 79–89.

    Google Scholar 

  • Revesz, R. Z. (2002). Introduction to Constraint Databases. Springer-Verlag.

    Google Scholar 

  • Rigaux, Ph., Scholl, M., and Voisard, A. (2000). Introduction to Spatial Databases: Applications to GIS. Morgan Kaufmann.

    Google Scholar 

  • Seidenberg, A. (1954). A new decision method for elementary algebra. Ann. of Math. (2), 60:365–374.

    Article  Google Scholar 

  • Stolboushkin, A.P. and Taitslin, M.A. (1996). Linear vs. order constraints over rational databases. In Proceedings of the 15th ACM Symposium on Principles of Database Systems, pages 17–27.

    Google Scholar 

  • Tarski, A. (1948). A Decision Method for Elementary Algebra and Geometry. University of California Press.

    Google Scholar 

  • TERA-project (1993). http://tera.medicis.polytechnique.fr/index.html.

  • van den Dries, L. (1998). Tame Topology and O-minimal Structures, volume 248 of London Mathematical Society Lecture Note Series. Cambridge University Press.

    Google Scholar 

  • Vandeurzen, L., Gyssens, M., and Van Gucht, D. (1996). On query languages for linear queries definable with polynomial constraints. In Freuder, E. F., editor, Proceedings of the 2nd Conference on Principles and practice of constraint programming, volume 1118 of Lecture Notes in Computer Science, pages 468–481, Berlin. Springer-Verlag.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Hasselt University, Belgium

    Floris Geerts & Bart Kuijpers

  2. Transnational University of Limburg, The Netherlands

    Floris Geerts & Bart Kuijpers

  3. University of Edinburgh, UK

    Floris Geerts

Authors
  1. Floris Geerts
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  2. Bart Kuijpers
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Editor information

Editors and Affiliations

  1. University of Groningen, The Netherlands

    Marco Aiello

  2. University of Manchester, UK

    Ian Pratt-Hartmann

  3. University of Amsterdam, The Netherlands

    Johan Van Benthem

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Geerts, F., Kuijpers, B. (2007). Real Algebraic Geometry and Constraint Databases. In: Aiello, M., Pratt-Hartmann, I., Van Benthem, J. (eds) Handbook of Spatial Logics. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-5587-4_13

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