Abstract
We consider spatial databases defined in terms of polynomial inequalities, and investigate the use of Datalog as a query language for such databases. Recursive programs are not guaranteed to terminate in this setting. Through a series of examples we show that useful restrictions on the databases under consideration or on the syntax of allowed programs, guaranteeing termination, are unlikely to exist. Hence, termination of particular recursive spatial queries must be established by ad-hoc arguments, if it can be established at all. As an illustration of the difficulties that can be encountered in this respect we discuss the topological connectivity query.
Post-doctoral research fellow of the Belgian National Fund for Scientific Research.
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References
D.S. Arnon. Geometric reasoning with logic and algebra. Artificial Intelligence, 37:37–60, 1988.
M. Benedikt, G. Dong, L. Libkin, and L. Wong. Relational expressive power of constraint query languages. In Proceedings 15th ACM Symposium on Principles of Database Systems. ACM Press, 1996.
J. Bochnak, M. Coste, and M.-F. Roy. Géométrie algébrique réelle. Springer-Verlag, 1987.
G.E. Collins. Quantifier elimination for real closed fields by cylindrical algebraic decomposition. Lecture Notes in Computer Science, 33:134–183, 1975.
M. Coste. Ensembles semi-algébriques. In Géometrie algébrique réelle et formes quadratiques, volume 959 of Lecture Notes in Mathematics, pages 109–138. Springer, 1982.
S. Grumbach and J. Su. First-order definability over constraint databases. In Montanari and Rossi [10], pages 121–136.
M. Gyssens, J. Paredaens, J. Van den Bussche, and D. Van Gucht. Computable queries for spatial database systems. In preparation.
P.C. Kanellakis, G.M. Kuper, and P.Z. Revesz. Constraint query languages. Journal of Computer and System Sciences, 51(1):26–52, August 1995.
E.E. Moise. Geometric topology in dimensions 2 and 3, volume 47 of Graduate Texts in Mathematics. Springer, 1977.
U. Montanari and F. Rossi, editors. Principles and practice of constraint programming, volume 976 of Lecture Notes in Computer Science. Springer, 1995.
J. Paredaens, J. Van den Bussche, and D. Van Gucht. Towards a theory of spatial database queries. In Proceedings 13th ACM Symposium on Principles of Database Systems, pages 279–288. ACM Press, 1994.
J. Renegar. On the computational complexity and geometry of the first-order theory of the reals. Journal of Symbolic Computation, 13, 1992.
P.Z. Revesz. A closed-form evaluation for Datalog queries with integer (gap)-order constraints. Theoretical Computer Science, 116:117–149, 1993.
P.Z. Revesz. Safe stratified Datalog with integer order programs. In Montanari and Rossi [10], pages 154–169.
J.T. Schwartz and M. Sharir. On the piano movers' problem II. In J.T. Schwartz, M. Sharir, and J. Hopcroft, editors, Planning, Geometry, and Complexity of Robot Motion, pages 51–96. Ablex Publishing Corporation, Norwood, New Jersey, 1987.
A. Tarski. A Decision Method for Elementary Algebra and Geometry. University of California Press, 1951.
J. Ullman. Principles of Database and Knowledge-Base Systems, volume I. Computer Science Press, 1988.
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Kuijpers, B., Paredaens, J., Smits, M., Van den Bussche, J. (1996). Termination properties of spatial Datalog programs. In: Pedreschi, D., Zaniolo, C. (eds) Logic in Databases. LID 1996. Lecture Notes in Computer Science, vol 1154. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0031737
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DOI: https://doi.org/10.1007/BFb0031737
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