On Query Languages for Linear Queries Definable with Polynomial Constraints

It has been argued that the linear database model in which semi linear sets are the only geometric objects is very suitable for most spatial database applications For querying linear databases the lan guage FO linear has been proposed We present both negative and positive results regarding the expressiveness of FO linear First we show that the dimension query is de nable in FO linear which allows us to solve several interesting queries Next we show the non de nability of a whole class of queries that are related to sets not de nable in FO linear This result both sharpens and generalizes earlier results independently found by Afrati et al and the present authors and demonstrates the need for more expressive linear query languages if we want to sustain the desirability of the linear database model In this paper we show how FO linear can be strictly extended within FO poly in a safe way Whether any of the proposed extensions is complete for the linear queries de nable in FO poly remains open We do show however that it is undecidable whether an expression in FO poly induces a linear query