Category-Theoretic Formulation of the Model-Based Systems Architecting Cognitive-Computational Cycle
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Engineering Systems Laboratory, Aeronautics and Astronautics Department, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
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Department of Computer & Information Science and Engineering, University of Florida, Gainesville, FL 32611, USA
*
Author to whom correspondence should be addressed.
Academic Editor: Anton Civit
Appl. Sci. 2021, 11(4), 1945; https://doi.org/10.3390/app11041945
Received: 12 December 2020 / Revised: 17 February 2021 / Accepted: 19 February 2021 / Published: 23 February 2021
(This article belongs to the Special Issue Model-Based Systems Engineering: Rigorous Foundations for Digital Transformations in Science and Engineering)
Simple Summary
This paper introduces a holistic framework, underpinned by Category Theory, for the process of conceptual modeling of complex engineered systems, generically representing the models as graph data structures, rendering stakeholder-informing views like matrices and visual graphs from the graph data structure, and reasoning about the visualized information in order to refine and enhance the concept of the system. This iterative process—a composition of a cognitive segment with a computational segment—proves to be an important formulation of the model-based systems architecting cycle.
We introduce the Concept→Model→Graph→View Cycle (CMGVC). The CMGVC facilitates coherent architecture analysis, reasoning, insight, and decision making based on conceptual models that are transformed into a generic, robust graph data structure (GDS). The GDS is then transformed into multiple views of the model, which inform stakeholders in various ways. This GDS-based approach decouples the view from the model and constitutes a powerful enhancement of model-based systems engineering (MBSE). The CMGVC applies the rigorous foundations of Category Theory, a mathematical framework of representations and transformations. We show that modeling languages are categories, drawing an analogy to programming languages. The CMGVC architecture is superior to direct transformations and language-coupled common representations. We demonstrate the CMGVC to transform a conceptual system architecture model built with the Object Process Modeling Language (OPM) into dual graphs and a stakeholder-informing matrix that stimulates system architecture insight.
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Keywords:
model-based systems engineering; category theory; object–process methodology; model analytics; concept–model–graph–view cycle; graph data structures
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MDPI and ACS Style
Mordecai, Y.; Fairbanks, J.P.; Crawley, E.F. Category-Theoretic Formulation of the Model-Based Systems Architecting Cognitive-Computational Cycle. Appl. Sci. 2021, 11, 1945. https://doi.org/10.3390/app11041945
AMA Style
Mordecai Y, Fairbanks JP, Crawley EF. Category-Theoretic Formulation of the Model-Based Systems Architecting Cognitive-Computational Cycle. Applied Sciences. 2021; 11(4):1945. https://doi.org/10.3390/app11041945
Chicago/Turabian StyleMordecai, Yaniv; Fairbanks, James P.; Crawley, Edward F. 2021. "Category-Theoretic Formulation of the Model-Based Systems Architecting Cognitive-Computational Cycle" Appl. Sci. 11, no. 4: 1945. https://doi.org/10.3390/app11041945
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