My research is at the intersection of three areas: (i) Temporal Logics, (ii) Declarative Problem Solving, and (iii) Process Mining. In particular, I focus on solving problems from Declarative Process Mining - where process models are temporal logic formulae - using declarative approaches like Satisfiability testing (SAT), Answer Set Programming (ASP), and Automated Planning (AP). My main result is the proposal of a new technique for Temporal Reasoning in ASP, based on exploiting the automata representation of the formulae, and that finds application to many Process Mining problems.