First-Order Definable Counting-Only Queries

For several practical queries on bags of sets of objects, the answer does not depend on the precise composition of these sets, but only on the number of sets to which each object belongs. This is the case k = 1 for the more general situation where the query answer only depends on the number of sets to which each group of at most k objects belongs. We call such queries k-counting-only. Here, we focus on k$$k$$-SyCALC, k-counting-only queries …