The triptych of conceptual modeling
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The triptych of conceptual modeling A framework for a better understanding of conceptual modeling Heinrich C. Mayr1
· Bernhard Thalheim2
Received: 23 September 2020 / Accepted: 23 September 2020 © The Author(s) 2020
Abstract We understand this paper as a contribution to the “anatomy” of conceptual models. We propose a signature of conceptual models for their characterization, which allows a clear distinction from other types of models. The motivation for this work arose from the observation that conceptual models are widely discussed in science and practice, especially in computer science, but that their potential is far from being exploited. We combine our proposal of a more transparent explanation of the nature of conceptual models with an approach that classifies conceptual models as a link between the dimension of linguistic terms and the encyclopedic dimension of notions. As a paradigm we use the triptych, whose central tableau represents the model dimension. The effectiveness of this explanatory approach is illustrated by a number of examples. We derive a number of open research questions that should be answered to complete the anatomy of conceptual models. Keywords Conceptual modeling · Modeling languages · Model characteristics · Model hierarchies · Language hierarchies · Concept · Notion · Term
1 Introduction Perception and abstraction, i.e., “modeling,” and reasoning on models are basic human capabilities for coping with, understanding, and influencing the environment. Over time, many types of modeling have evolved: from completely intuitive to highly controlled ones that apply a specific set of terms forming the semantic instruments of a (modeling) language. Natural language enables us to describe, communicate, or understand perceptions and thus supports a moderately controlled modeling: the language elements (words, phrases, texts, icons), their composition, and meaning are tacitly agreed upon by the users and, to a certain degree, are shared among them. The assignment of meaning to language elements, however, is sometimes ambiguous, and the syntactical rules are not strict throughout. Elements, syntax, and interpretation change over time.
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Heinrich C. Mayr [email protected]
In contrast to that, scientific disciplines, in particular mathematics, introduce strict formal languages and propose semantic interpretations to the lexical elements and their syntactic composition. An illustrative example of such a formal approach is the Petri Net Language as initially introduced by Petri [1]: a special type of bipartite directed graphs is provided together with some composition rules, and a family of functions (“marking” and “transition”). Applying standard Linear Algebra mechanisms to this leads to a powerful calculus. However, this calculus has no semantics at all! In order to make Petri Nets usable for modeling, we need to provide a “net interpretation,” i.e., to associate semantics to the language elements. Most popular is to interpret one type of nodes (the places) by Conditions an
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