First-Order Query Evaluation with Cardinality Conditions

We study an extension of first-order logic that allows to express cardinality conditions in a similar way as SQL’s COUNT operator. The corresponding logic FOC(P) was introduced by Kuske and Schweikardt [16], who showed that query evaluation for this logic is fixedparameter tractable on classes of databases of bounded degree. In the present paper, we first show that the fixed-parameter tractability of FOC(P) cannot even be generalised to very simple classes of databases of unbounded degree such as unranked trees or strings with a linear order relation. Then we identify a fragment FOC1(P) of FOC(P) which is still sufficiently strong to express standard applications of SQL’s COUNT operator. Our main result shows that query evaluation for FOC1(P) is fixed-parameter tractable on nowhere dense classes of databases.