Abstract
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.
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Notes
- 1.
is the granule preorder defined in the granule assignment 
(see Summary 2.3) while 
is the general subsumption relation used to define rules. For 
, it is always the case that 
implies 
. The converse is not required to hold, although in practice it usually does.
is the granule preorder defined in the granule assignment 
(see Summary 
is the general subsumption relation used to define rules. For 
, it is always the case that 
implies 
. The converse is not required to hold, although in practice it usually does.References
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Acknowledgment
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.
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Hegner, S.J., Rodríguez, M.A. (2018). Implicit Representation of Bigranular Rules for Multigranular Data. In: Hartmann, S., Ma, H., Hameurlain, A., Pernul, G., Wagner, R. (eds) Database and Expert Systems Applications. DEXA 2018. Lecture Notes in Computer Science(), vol 11029. Springer, Cham. https://doi.org/10.1007/978-3-319-98809-2_23
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