Informatics and Applications

2018, Volume 12, Issue 1, pp 95-104

CATEGORY THEORY AS A MATHEMATICAL PRAGMATICS OF MODEL-BASED SYSTEMS ENGINEERING

S. Kovalyov

Abstract

Mathematical device built upon the category theory is developed which was previously proposed to formally describe and rigorously explore procedures of employing models in engineering that constitute the pragmatics of model-based systems engineering. The essence of the device consists in mathematical representation of assembly drawings (megamodels of systems) as diagrams in categories whose objects are models, and morphisms represent actions associated with assembling system models from component models. Category-theoretical methods for solving direct and inverse pragmatic problems of assembling systems are proposed and explored. The key role of the diagram monad is revealed. Special attention is paid to the problem of recovering the configuration of a given system, taking into account technological limitations of the assembling means and procedures. A number of key systems engineering concepts are matched with relevant constructions of the category theory

[+] References (20)

Gianni, D., A. D'Ambrogio, and A. Tolk, eds. 2014. Modeling and simulation-based systems engineering handbook. London: CRC Press. 513 p.
Selic, B. 2003. The pragmatics of model-driven development. IEEE Software 20(5):19-25.
Levenchuk, A.I. 2015. Sistemnoinzhenernoe myshlenie [Systems engineering thinking]. Moscow: TechInvestLab. 305 p.
Kovalyov, S. P 2017. Metody teorii kategoriy v model'no- orientirovannoy sistemnoy inzhenerii [Methods of category theory in model-based systems engineering]. Informatika i ee Primeneniya - Inform. Appl. 11(3):42-50.
IEC 81346-1:2009. 2009. Industrial Systems, Installations and Equipment and Industrial Products - Structuring Principles and Reference Designations - Part 1: Basic Rules. Geneva: ISO. 168 p.
Ginali, S., and J. Goguen. 1978. A categorical approach to general systems. Applied general systems research: Recent development and trends. Ed. G. J. Klir. NATO conference ser. Boston, MA: Springer U.S. 5:257-270.
Diskin, Z., S. Kokaly, and T. Maibaum. 2013. Mapping- aware megamodeling: Design patterns and laws. Software language engineering: 6th Conference (International) Proceedings. Eds. M. Erwig, R. F. Paige, and E. Van Wyk. Lecture notes in computer science ser. Springer. 8225:322343.
Kossiakoff, A., W. N. Sweet, S. Seymour, and S.M. Biemer. 2011. Systems engineering principles and practice. 2nd ed. New York, NY: John Wiley. 560 p.
Bezivin, J., F Jouault, P. Rosenthal, and P. Valduriez. 2005. Modeling in the large and modeling in the small. Model driven architecture: European MDA Workshops on Foundations and Applications Proceedings. Eds. U. Afimann, M. Aksit, and A. Rensink. Lecture notes in computer science ser. Springer. 3599:33-46.
Neema, S., J. Sztipanovits, G. Karsai, and K. Butts. 2003. Constraint-based design-space exploration and model synthesis. 3rd Conference (International) on Embedded Software Proceedings. Eds. R. Alur and I. Lee. Lecture notes in computer science ser. Springer. 2855:290-305.
Vanherpen, K., J. Denil, P. De Meulenaere, and H. Vangheluwe. 2014. Design-space exploration in MDE: An initial pattern catalogue. 1st Workshop (International) on Combining Modelling with Search- and Example-Based Approaches Proceedings. Eds. R. Paige, M. Kessentini, P. Langer, and M. Wimmer. CEUR Workshop Proceedings ser. Valencia, Spain. 1340:42-51.
GOST 14.205-83. 2009. Tekhnologichnost' konstruktsii izdeliy. Terminy i opredeleniya [Technological efficiency of products design. Terms and definitions]. Moscow: Standardinform Publs. 22 p.
Altshuller, G. 1984. Creativity as an exact science: The theory of the solution of inventive problems. Amsterdam: Gordon and Breach Science Publs. 324 p.
Guitart, R., and L. van den Bril. 1977. Decompositions et lax-completions. Cah. Topologie Geometrie Differentielle Categoriques 18(4):333-407.
Adamek, J., H. Herrlich, and G.E. Strecker. 1990. Abstract and concrete categories. New York, NY: John Wiley. 507 p.
Mac Lane, S. 1978. Categories for the working mathematician. New York, NY: Springer. 317 p.
Andryushkevich, S. K., S. S. Zhuravlev, E. P. Zolotukhin, S. P. Kovalyov, V. V. Okol'nishnikov, and S. V. Rudometov. 2010. Razrabotka sistemy monitoringa s ispol'zovaniem imitatsionnogo modelirovaniya [Development of a monitoring system using simulation]. Problemy informatiki [Problems of Informatics] 4:65-75.
Baez, J., and M. Stay. 2011. Physics, topology, logic and computation: A Rosetta stone. New structures for physics. Ed. B. Coecke. Lecture notes in physics ser. Springer. 813:95-172.
Kovalev, S. P. 2013. Systems analysis of life cycle of large- scale information-control systems. Automat. Rem. Contr. 74(9):1510-1524.
Gross, J., A. Chlipala, and D. I. Spivak. 2014. Experience implementing a performant category-theory library in Coq. 5th Conference (International) on Interactive Theorem Proving Proceedings. Eds. G. Klein and R. Gamboa. Lecture notes in computer science ser. Springer. 8558:275-291.

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