Implicit Representation of Bigranular Rules for Multigranular Data

  • Stephen J. HegnerEmail author
  • M. Andrea Rodríguez
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11029)


Domains for spatial and temporal data are often multigranular in nature, possessing a natural order structure defined by spatial inclusion and time-interval inclusion, respectively. This order structure induces lattice-like (partial) operations, such as join, which in turn lead to join rules, in which a single domain element (granule) is asserted to be equal to, or contained in, the join of a set of such granules. In general, the efficient representation of such join rules is a difficult problem. However, there is a very effective representation in the case that the rule is bigranular; i.e., all of the joined elements belong to the same granularity, and, in addition, complete information about the (non)disjointness of all granules involved is known. The details of that representation form the focus of the paper.



The work of M. Andrea Rodríguez, as well as three visits of Stephen J. Hegner to Concepción, during which many of the ideas reported here were developed, were funded in part by Fondecyt-Conicyt grant number 1170497.


  1. 1.
    Bettini, C., Dyreson, C.E., Evans, W.S., Snodgrass, R.T., Wang, X.S.: A glossary of time granularity concepts. In: Etzion, O., Jajodia, S., Sripada, S. (eds.) Temporal Databases: Research and Practice. LNCS, vol. 1399, pp. 406–413. Springer, Heidelberg (1998). Scholar
  2. 2.
    Camossi, E., Bertolotto, M., Bertino, E.: A multigranular object-oriented framework supporting spatio-temporal granularity conversions. Int. J. Geogr. Inf. Sci. 20(5), 511–534 (2006)CrossRefGoogle Scholar
  3. 3.
    Davey, B.A., Priestly, H.A.: Introduction to Lattices and Order, 2nd edn. Cambridge University Press, Cambridge (2002)CrossRefGoogle Scholar
  4. 4.
    Egenhofer, M.J.: Deriving the composition of binary topological relations. J. Vis. Lang. Comput. 5(2), 133–149 (1994)CrossRefGoogle Scholar
  5. 5.
    Euzenat, J., Montanari, A.: Time granularity. In: Fisher, M., Gabbay, D.M., Vila, L. (eds.) Handbook of Temporal Reasoning in Artificial Intelligence, vol. 1, pp. 59–118. Elsevier, New York (2005)CrossRefGoogle Scholar
  6. 6.
    Fagin, R.: Horn clauses and database dependencies. J. Assoc. Comp. Mach. 29(4), 952–985 (1982)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Hegner, S.J., Rodríguez, M.A.: Integration integrity for multigranular data. In: Pokorný, J., Ivanović, M., Thalheim, B., Šaloun, P. (eds.) ADBIS 2016. LNCS, vol. 9809, pp. 226–242. Springer, Cham (2016). Scholar
  8. 8.
    Hegner, S.J., Rodríguez, M.A.: A model for multigranular data and its integrity. Informatica Lith. Acad. Sci. 28, 45–78 (2017)Google Scholar
  9. 9.
    Kifer, M., Bernstein, A., Lewis, P.M.: Database Systems: An Application-Oriented Approach, 2nd edn. Addison-Wesley, Boston (2006)Google Scholar
  10. 10.
    Mach, M.A., Owoc, M.L.: Knowledge granularity and representation of knowledge: towards knowledge grid. In: Shi, Z., Vadera, S., Aamodt, A., Leake, D. (eds.) IIP 2010. IAICT, vol. 340, pp. 251–258. Springer, Heidelberg (2010). Scholar
  11. 11.
    Monk, J.D.: Mathematical Logic. Springer, New York (1976). Scholar
  12. 12.
    Wang, S., Liu, D.: Spatio-temporal database with multi-granularities. In: Li, Q., Wang, G., Feng, L. (eds.) WAIM 2004. LNCS, vol. 3129, pp. 137–146. Springer, Heidelberg (2004). Scholar

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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.DBMS Research of New HampshireNew LondonUSA
  2. 2.Millennium Institute for Foundational Research on Data, Departamento Ingeniería Informática y Ciencias de la ComputaciónUniversidad de ConcepciónConcepciónChile

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