The temporal feature integrated temporal attributes into Odysseus. These can be useful to predict unknown or future values of an attribute that develops over time. The temporal feature brings a complete semantics for temporal processing and is the foundation for spatio-temporal processing in Odysseus. The temporal feature is closely related to the moving object algebra by Güting et al.

Temporal Attributes

Temporal attributes are attributes that not only have one value, but one value for each point in time for a certain time interval. In other words, a temporal attribute of a certain type is a function that for each point in time returns a value of its type. Take a temporal integer over the interval [0,5) as an example. It could be the function f(t) = 5 * t. Then, it has five values, one for each point in the time interval: 0→ 0, 1→ 5, 2→ 10, 3→ 15, 4→ 20. A temporal integer can be denoted as tinteger, a temporal boolean as tboolean and so on.

Internally, for Odysseus, a temporal attribute looks just like a non-temporal attribute. For example, a temporal integer looks like an integer for Odysseus. Nevertheless, the temporal feature tricks Odysseus a little bit at this point. While the type in the schema stays an integer, the actual value is not an integer but a temporal integer. In the schema, a temporal attribute can be detected in the constraints, which is a key-value field each attribute has. Here, temporal is set to true.

Prediction Time Interval and Bitemporal Streams

The previously mentioned time interval for which a temporal attribute has the values is the Prediction Time Interval. It is an additional time interval in the metadata of a stream element next to the normal stream time interval. It needs to be activated in the metadata definition of a query:

metaattribute = ['TimeInterval',  'PredictionTimes'],

As you can see, the metadata is called PredictionTimes. That is because in fact the metadata holds a list of non-overlapping time intervals. That is due to the algebra behind this approach and is explained later on.

With two time intervals, the stream time (TimeInterval) and the prediction time, we have two temporal dimensions for each stream element. We denote this as a bitemporal stream.

Lifted Expressions

Lifted expressions are normal expressions with at least one temporal attribute involved.

Theoretical Foundation

Expressions are a core element of queries. They are used in map, select, and join operators. Typically, an expression uses one or more attributes from the stream element(s). An example could be attribute1 + attribute2 > 42. A goal of the temporal feature is that this works with temporal attributes in the same way it does with non-temporal attributes. This is done with the lifting approach (a term from the moving object algebra). If at least one attribute of an expression is temporal, the output of the expression will also be temporal. This can be denoted with a second order signature.

Let us consider two functions: distance, in_interior (both are spatial, wherefore you would additionally need to use the spatial feature. Also consider the spatio-temporal feature.) and +.

point × region → boolean [in_interior]

point × point → real [distance]

real × real → real [+]

The lifting process now creates all combinations wil temporal attributes.

tpoint × region → tboolean [in_interior]

point × tregion → tboolean [in_interior]

tpoint × tregion → tboolean [in_interior]

tpoint × point → treal [distance]

point × tpoint → treal [distance]

tpoint × tpoint → treal [distance]

treal × real → treal [+]

real × treal → treal [+]

treal × treal → treal [+]

Handling of Lifted Expressions in Odysseus

The idea behind the temporal feature is that you can use any normal function and the function does not need to know about the temporal feature. This is achieved by a simple trick: the non-temporal version of the expression is automatically evaluated for each point in time in the prediction time interval. The temporal attributes are solved for the points in time, create a non-temporal value which is then used to evaluate the function in a non-temporal manner. Then, the single results are stacked together to create a temporal output attribute. This is what the temporal feature does for you so you don't have to worry about this when writing your expressions.

The translation rules for the single operators detect if a temporal attribute is used in the expression(s). Then, a TemporalRelationalExpression is created instead if a RelationalExpression. The output of a temporal expression is typically a GenericTemporalType. Because it is not feasible to always create a temporal function, a simple map is used that maps from the time to the values. This new temporal attribute can of course be used in other expressions with any kind of function.

Direct Temporal Functions

The moving object algebra defines some functions that work directly on temporal attributes and therefore do not need this kind of translation described above. An example would be the SpeedFunction from the spatio-temporal feature. It takes a temporal spatial point (tpoint) and creates a tdouble with the speed of the object at each point in time.

Limitations

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Operators

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PredictionTime

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Map

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Select

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Join

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Aggregate

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Examples

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