We propose Answer Set Programming (ASP) as an approach for modeling and solving problems from the area of Declarative Process Mining (DPM). We consider here three classical problems, namely, Log Generation, Conformance Checking, and Query Checking. These problems are addressed from both a control-flow and a data-aware perspective. The approach is based on the representation of process specifications as (finite-state) automata. Since these are strictly more expressive than the defacto DPM standard specification language DECLARE, more general specifications than those typical of DPM can be handled, such as formulas in linear-time temporal logic over finite traces.