An IP-table for one or more temporal relations stores information about the temporal structure of the time intervals appearing in these relations. An IP-table is specific to those temporal relations. Figure 7.1 shows the definition of an IP-table for a temporal relation R; the definition for two or more relations works accordingly.
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tj-1 < tj for
.We note that an IP-table can be considered as a relation itself. Thus IP-tables which represent a form of metadata are represented in the same logical data model as the data itself. This means that metadata can be accessed in the same way as the data. Many other forms of metadata can also be represented as relations [Date, 1995]. It is a nice side-effect that IP-tables stand in harmony with this generally welcomed feature of relational databases.
In section 7.3, we show how N can be reduced if the IP-table becomes too big. This leads to two variations of the IP-table definition. We will then refer to the original version - as defined in figure 7.1 - as a complete IP-table .
As mentioned above, we could alternatively use any pair of the values , , , for an IP-table. The missing ones can then be derived by using the equations of figure 5.1. Please note the following: because of the third observation made in section 7.1 it is
for . Consequently, equation (5.2) can be applied as| (24) |
Figure 7.2 shows the example for timestamp intervals of a temporal relation R that has already been used in chapter 5. Intervals are represented as bold bars connecting their start- and endpoint respectively. Figure 7.3 shows the corresponding IP-table I(R) for R (in bold typeface) plus the derivable values and for demonstration purposes.