Declarative business process (BP) models define the behavior of BPs as a set of temporal constraints, which can be summarized as a deterministic finite state automaton (DFA). Declarative BP discovery aims at inferring such constraints from event logs. To this aim, it requires as additional input the set of candidate constraints to be verified with respect to the event log. Intuitively, this restricts the discovery task to a conformance checking activity between a predefined set of constraint templates and an event log, preventing to learn any observed behavior that is not captured by those templates. In this paper, we investigate how to leverage Model Learning (ML) for the automated discovery of the DFA underlying the behavior of a declarative BP model, without using any further a-priori information in addition to the event log. To assess the quality of the discovered DFA, we introduce a novel definition of the standard process mining quality metrics, i.e., precision, generalization and simplicity, tailored to DFAs. Finally, a preliminary evaluation performed with real-life logs shows that ML enables to generate extremely simpler DFAs than state-of-the-art BP declarative discovery techniques, keeping similar values of precision and generalization.