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Domain learning is the task of finding an action model that can explain given observed plan executions, so-called traces. It allows us to automate the identification of actions' preconditions and effects instead of relying on hand-modeled expert knowledge. While previous research has put forth various techniques and covers multiple planning formalisms, the theoretical foundations of domain learning are still in their infancy. We investigate the most basic setting, that is grounded classical planning without negative preconditions or conditional effects with full observability of the state variables. The given traces are assumed to be justified in the sense that either no single action or no set of actions can be removed without violating correctness of the plan. Furthermore, we might be given additional constraints in the form of a propositional logical formula. We show the consequences of these assumptions for the computational complexity of identifying a satisfactory planning domain.