Order Independent Temporal Properties

Abstract

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.