Order Independent Temporal Properties

The paper investigates temporal properties that are invariant with respect to the temporal ordering and that are expressible by temporal query languages either explicit like FO(≤) or implicit like TL. In the case of an explicit time representation, these 'order invariant' temporal properties are simply those expressible in the language FO(=). In the case of an implicit time representation, we introduce a new language, TL(Ei) that captures exactly these properties. The expressive power of the language TL(Ei) is characterized via a game a la Ehrenfeucht-Fraisse. This provides another proof, using a more classical technique, that the implicit temporal language TL is strictly less expressive than the explicit temporal language FO(≤). This alternative proof is interesting by itself and opens new perspectives in the investigation of results of the same kind for more expressive implicit temporal languages than TL.