  In this article, we study the complexity of weighted team definability for
logics with team semantics. This problem is a natural analogue of one of the
most studied problems in parameterized complexity, the notion of weighted
Fagin-definability, which is formulated in terms of satisfaction of first-order
formulas with free relation variables. We focus on the parameterized complexity
of weighted team definability for a fixed formula phi of central team-based
logics. Given a first-order structure A and the parameter value k as input, the
question is to determine whether A,T models phi for some team T of size k. We
show several results on the complexity of this problem for dependence,
independence, and inclusion logic formulas. Moreover, we also relate the
complexity of weighted team definability to the complexity classes in the
well-known W-hierarchy as well as paraNP.
