We put forward Answer Set Programming (ASP) as a solution approach for three classical problems in Declarative Process Mining: Log Generation, Query Checking, and Conformance Checking. These problems correspond to different ways of analyzing business processes under execution, starting from sequences of recorded events, a.k.a. event logs. We tackle them in their data-aware variant, i.e., by considering events that carry a payload (set of attribute-value pairs), in addition to the performed activity, specifying processes declaratively with an extension of linear-time temporal logic over finite traces (LTLf). The data-aware setting is significantly more challenging than the control-flow one: Query Checking is still open, while the existing approaches for the other two problems do not scale well. The contributions of the work include an ASP encoding schema for the three problems, their solution, and experiments showing the feasibility of the approach.