In valid-time indeterminacy, it is known that an event stored in a temporal database did in fact occur, but it is not known exactly when the event occurred. We extend a tuple-timestamped temporal data model to support valid-time indeterminacy and outline its implementation. This work is novel in that previous research, although quite extensive, has not studied this particular kind of incomplete information. To model the occurrence time of an event, we introduce a new data type called an indeterminate instant. Our thesis is that by representing an indeterminate instant with a set of contiguous chronons and a probability distribution over that set, it is possible to characterize a large number of (possibly weighted) alternatives, to devise intuitive query language constructs, including schema specification, temporal constants, temporal predicates and constructors, and aggregates, and to implement these constructs efficiently. We extend the TQuel and TSQL2 query languages with constructs to retrieve information in the presence of indeterminacy. Although the extended data model and query language provide needed modeling capabilities, these extensions appear to carry a significant execution cost. The cost of support for indeterminacy is empirically measured, and is shown to be modest. We then show how indeterminacy can provide a much richer modeling of granularity and now. Granularity is the unit of measure of a temporal datum (e.g., days, months, weeks). Indeterminacy and granularity are two sides of the same coin insofar as a time at a given granularity is indeterminate at all finer granularities. Now is a distinguished temporal value. We describe a new kind of instant, a now-relative indeterminate instant, which has the same storage requirements as other instants, but can be used to model situations such as that an employee is currently employed but will not work beyond the year 1995. In summary, support for indeterminacy dramatically increases the modeling capabilities of a temporal database without adversely impacting performance.
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