The Expressive Power of the Temporal Query Language Lh

Temporal knowledge representation and reasoning methods require expressive power — which ensures usefulness in non-trivial applications as well as reasonable complexity, which guarantees efficient implementation. The temporal language LH [7, 4, 8, 5] is an attempt to find a balance between expressive power and complexity. LH serves as a means for expressing temporal constraints over the properties of a domain, such as:’x is a device which has been operating during the same time device y was operating“. In this paper, we show that LH is expressive enough to allow defining temporal connectivity queries, which in turn cannot be defined in First-Order Logic (FOL). The methodology which we use relies on Ehrenfeucht-Fraı̈ssé-games. This formal result is of practical interest, because it shows that LH cannot be embedded in a relational database schema relying on FOL. The rest of the paper is structured as follows: in Section 2 we introduce temporal graphs and in Section 3 — the language LH. In Section 4 we examine the expressive power of LH. To this end, we show that LH is expressive enough to capture connectivity constraints. In contrast, in Section 5 we show FOL is unable to express such constraints. Finally, in Section 6, we conclude.