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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.

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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

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 [+]Text

Operators

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Map

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Select

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