Title: Designing an appropriate logic for conceptual modelling languages Abstract: Logic-based reconstructions of conceptual data modelling languages for computing, such as UML, EER, and ORM, are abound and there are many more logics to choose from. This raises the question as to which of them, if any, is actually a good logic that is at least fit for purpose, and, following from that, when is a logic "good". In order to address this, we adapt the methodological approach of DSL language design to the development of logics for conceptual data modelling and extend it with a step concerning ontological analysis of core language design choices. This is then applied to formally specify logic-based conceptual data modelling profiles and three algorithms to harmonize fundamentally alternate design choices for the logics.