This article frames Conceptual Modeling education as a design problem, in the sense of the Design Science research framework, motivated by student preconceptions and oversimplifications causing a gap between how the discipline is perceived at bachelor level and the holistic understanding of model value that is required for research work. The treatment to this design problem must comprise teaching approaches and artifacts capable of positioning Conceptual Modeling as a standalone discipline having a value proposition for any application domain, rather than a technique subordinated to other disciplines. The underpinning thesis is that modeling languages should be primarily understood as purposeful knowledge schemas that can be subjected to agile adaptations in support of model-driven systems or knowledge processes, by analogy to how a database schema is evolved in response to changing requirements of a data-driven system or data analytics needs. This thesis is supported by enablers provided by the Open Models Laboratory and the Agile Modeling Method Engineering frameworkresources that support the development of treatments to the design problem framed by the article.

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. In this paper we build on the widely accepted approach of logic as basis for modeling languages and define them as languages in the sense of typed predicate logic comprising a signature Σ and a set of constraints. We concretize how the basic concepts of a language -object and relation types, attributes, inheritance and constraints -can be expressed in logical terms. This naturally leads to the denotation of a model as Σ-structure satisfying all constraints. We apply this definition also on the metalevel and propose a formal modeling language to specify metamodels called M2FOL. A thus formalized metamodel then rigorously defines the signature of a language and we provide an algorithmic derivation of the formal modeling language from the metamodel. The effectiveness of our approach is demonstrated by formalizing the Petri Net modeling language, a method frequently used for analysis and simulation in enterprise modeling.

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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 formalism MetaMorph based 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. MetaMorph defines 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 the MetaMorph formalism 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 the MetaMorph formalism. This shows that the rich knowledge stack on formal languages in logic offers new tools for old problems.

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