Abstract Models have evolved from mere pictures supporting human understanding and communication to sophisticated knowledge structures processable by machines and establish value through their processing capabilities. This entails an inevitable need for computer-understandable modeling languages and causes formalization to be a crucial part in the lifecycle of engineering a modeling method. An appropriate formalism must be a means for providing a structural definition to enable a theoretical investigation of conceptual modeling languages and a unique, unambiguous way of specifying the syntax and semantics of an arbitrary modeling language. For this purpose, it must be generic and open to capturing any domain and any functionality. This paper provides a pervasive description of the formalism MetaMorph based on logic and model theory—an approach fulfilling the requirements above for modeling method engineering. The evaluation of the formalism is presented following three streams of work: First, two evaluative case studies illustrate the applicability of MetaMorph formalism concept by concept on the modeling language ProVis from the domain of stochastic education and the well-known Entity-Relationship language. ProVis as well as ER comprise only a few objects and relation types but with high interconnection and expressive power and are therefore considered interesting specimens for formalization. Second, a comprehensive juxtaposition of MetaMorph to three other formalization approaches based on different foundational theories is outlined concept by concept to underpin the formalism design. Third, an empirical evaluation has been performed, assessing the usability and adequacy of the formalism within a classroom assessment. The results allow for conclusions on the completeness, intuitiveness, and complexity as well as on interdependencies with engineers’ skills.

Abstract Enterprise modeling deals with the increasing complexity of processes and systems by operationalizing model content and by linking complementary models and languages, thus amplifying the model value beyond mere comprehensible pictures. To enable this amplification and turn models into computer-processable structures, a comprehensive formalization is needed. This paper presents the formalismMetaMorphbased on typed first-order logic and provides a perspective on the potential and benefits of formalization that arise for a variety of research issues in conceptual modeling.MetaMorphdefines modeling languages as formal languages with a signature $$\varSigma $$ Σ —comprising object types, relation types, and attributes through types and function symbols—and a set of constraints. Four case studies are included to show the effectiveness of this approach. Applying theMetaMorphformalism to the next level in the hierarchy of models, we create , a formal modeling language for metamodels. We show that is self-describing and therefore complete the formalization of the full four-layer metamodeling stack. On the basis of our generic formalism applicable to arbitrary modeling languages, we examine four current research topics—modeling with power types, language interleaving & consistency, operations on models, and automatic translation of formalizations to platform-specific code—and how to approach them with theMetaMorphformalism. This shows that the rich knowledge stack on formal languages in logic offers new tools for old problems.