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A Formal Foundation of Systems Engineering

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Complex Systems Design & Management

Abstract

In this paper we discuss a formal foundation of systems engineering based on category theory. The main difference with other categorical approaches is the choice of the structure of the base category (symmetric monoidal or compact closed) which is, on the one hand, much better adapted to current modeling tools and languages (e.g. SysML), and on the other hand is canonically associated to a logic (linear logic or fragments thereof) that fits better with systems engineering. Since that logic has also a rich proof theory, this allows us to propose a global formal framework that encompasses: system modeling, system specification, and property verification.

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References

  1. Abramsky, S., Gay, S., Nagarajan, R.: Interaction categories and the foundations of typed concurrent programming. In: Proceedings of the 1994 Marktoberdorf Summer School. NATO ASI Series. Springer (1995)

    Google Scholar 

  2. Alexiev, V.: Applications of linear logic to computation: an overview. TR93-18, Univ. of Alberta, Canada (1993)

    Google Scholar 

  3. Baez, J.: Categories in control. Talk at Erlangen University. Downloadable as johncarlosbaez.wordpress.com/2014/02/06/categories-in-control (2014)

    Google Scholar 

  4. Baez, J., Erbele, J.: Categories in control. Downloadable as arXiv.1405.6881v1[math.CT] (2014)

    Google Scholar 

  5. Brown, C.: Relating Petri nets to formulae of linear logic. LFCS Report Series ECS-LFCS-89-87, Univ. of Edinburgh (1989)

    Google Scholar 

  6. Brown, C., Gurr, D., de Paiva, V.: A linear spcification language for Petri nets. TR-DAIMI-PB-363, Univ. of Aarhus (1991)

    Google Scholar 

  7. Cattani, G.L., Winskel, G.: Presheaf models for concurrency. In: van Dalen, D., Bezem, M. (eds.) CSL 1996. LNCS, vol. 1258, pp. 58–75. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  8. Bagnol, M., Guatto, A.: Synchronous machines: a traced category. Draft downloadable as hal.inria.fr/hal-00748010 (2012)

    Google Scholar 

  9. Coecke, B., Paquette, E.O.: Categories for the practising physicist. Downloadable as arXiv.0905.3010v2[quant-ph] (2009)

    Google Scholar 

  10. Engberg, U.H., Winskel, G.: Linear logic on Petri nets. BRICS Report Series RS-94-3, Univ. of Aarhus (1994)

    Google Scholar 

  11. Fiadeiro, J.L.: Categories for Software Engineering. Springer, Berlin (2005)

    MATH  Google Scholar 

  12. Fiori, C.: A first course in topos quantum theory. Lecture Notes in Physics, vol. 868. Springer (2013)

    Google Scholar 

  13. Girard, J.-Y.: Linear logic. Theoretical Computer Science, London Mathematical 50(1), 1–102 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  14. Golden, B., Aiguier, M., Krob, D.: Complex systems modeling II: a minimalist and unified semantics for heterogeneous integrated systems. Applied Mathematics and Computation 218(16), 8039–8055 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  15. Golden, B.: A unified formalism for complex systems architecture. Ph.D. in Computer Science, Ecole Polytechnique (2013)

    Google Scholar 

  16. Goguen, J.: Categorical foundations for systems theory. In: Pichler, F., Trappl, R. (eds.) Advances in Cybernetics and Systems Research, pp. 121–130. Transcripta Books (1973)

    Google Scholar 

  17. Goguen, J.: A categorical manifesto. Mathematical Structures in Computer Science 1(1), 49–67 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  18. Goguen, J.: Sheaf semantics for concurrent interacting objects. Mathematical Structures in Computer Science 11 (1992)

    Google Scholar 

  19. Grosu R., Stauner T.: Modular and visual specifications of hybrid systems: an introduction to HyCharts. TUM-I9801, Technische Universität München (1998)

    Google Scholar 

  20. Grosu, R., Broy, M., Selic, B., Stefanescu, G.: What is behind UML-RT? In: Behavioral Specifications of Businesses and Systems, pp. 73–88 (1999)

    Google Scholar 

  21. Heunen, C., Sadrzadeh, M., Grefenstetter, E.: Quantum physics and linguistics. Oxford University Press (2013)

    Google Scholar 

  22. Jacobs, B.: From coalgebraic to monoidal traces. Electric Notes in Theoretical Computer Science Proceedings of Coalgebraic Methods in Computer Science (2010)

    Google Scholar 

  23. Joyal, A., Street, R., Verity, D.: Traced monoidal categories. Math. Proc. Camb. Phil. Soc., vol. 119, pp. 447–468 (1996)

    Google Scholar 

  24. Katis, P., Sabadini, N., Walters, R.F.C.: Bicategories of processes. Journal of Pure and Applied Algebra 115, 141–178 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  25. Katis P., Sabadini N., Walters R.F.C.: On the algebra of feedback and systems with boundary. Rendiconti del Circolo Matematico di Palermo, Serie II (suppl. 63) (1999)

    Google Scholar 

  26. Luzeaux, D.: Towards the engineering of complex systems. Journées Nîmes 98 sur les Systèmes complexes, systèmes intelligents et interfaces, Nîmes, France (1998)

    Google Scholar 

  27. Luzeaux, D.: Category theory applied to digital systems theory. In: 4th World Multiconference on Systemics, Cybernetics, and Informatics, Orlando, FL, USA (1998)

    Google Scholar 

  28. Luzeaux, D.: Vers une nouvelle théorie abstraite des systèmes en vue de leur ingénierie. In: 5e conférence annuelle d’ingénierie système de l’AFIS, Paris (2009)

    Google Scholar 

  29. Mac Lane, S.: Categories for the working mathematician, 1st edn. Springer, New York (1971)

    Book  MATH  Google Scholar 

  30. Mac Lane, S.: Categories for the working mathematician, 2nd edn. Springer, New York (1998)

    MATH  Google Scholar 

  31. Mac Lane, S., Moerdijk, I.: Sheaves in geometry and logic: a first introduction to topos theory. Springer (1968)

    Google Scholar 

  32. Malherbe, O., Scott, P., Selinger, P.: Presheaf models of quantum computation: an outline. Downloadable as arXiv:1302.5652v1 (2013)

    Google Scholar 

  33. Moggi, E.: Notions of computations and monads. Information and Computation 93(1), 55–92 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  34. Nielsen, M., Sassone, V., Winskel, G.: Relationships between models of concurrency. In: de Bakker, J.W., de Roever, W.-P., Rozenberg, G. (eds.) REX 1993. LNCS, vol. 803, pp. 425–476. Springer, Heidelberg (1994)

    Chapter  Google Scholar 

  35. Pavlovic, D.: Tracing the man in the middle in monoidal categories. Downloadable as arXiv:1203.6324v1 (2012)

    Google Scholar 

  36. Rao, J., Küngas, P., Matskin, M.: Composition of semantic Web services using linear logic therorem proving. Information Systems 31, 340–360 (2006)

    Article  Google Scholar 

  37. Sassone, V.: An axiomatization of the category of Petri net computations. Mathematical Structures in Computer Science 8, 117–151 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  38. Selinger, P.: Categorical structure of asynchrony. Electric Notes in Theoretical Computer Science 20 (1999)

    Google Scholar 

  39. Selinger, P.: A survey of graphical languages for monoidal categories. Downloadable as arXiv:0908.3347v1 (2009)

    Google Scholar 

  40. Slodicak, V.: Toposes are symmetric monoidal closed categories. Scientific Research of the Institute of Mathematics and Computer Science 1(11), 107–116 (2012)

    Google Scholar 

  41. Winskel, G.: Petri net algebras, morphisms and compositionality. Information and Computation, 197–238 (1987)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Deputy Director, DIRISI, Ministry of Defense, Paris, France

    Dominique Luzeaux

Authors
  1. Dominique Luzeaux
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Correspondence to Dominique Luzeaux .

Editor information

Editors and Affiliations

  1. Département Informatique, Supélec, Gif-sur-Yvette cedex, France

    Frédéric Boulanger

  2. LIX/DIX, Ecole Polytechnique, Palaiseau Cedex, France

    Daniel Krob

  3. CRAN UMR 7039 Campus Sciences - BP 70239, Université de Lorraine, Vandœuvre-lès-Nancy, France

    Gérard Morel

  4. Airbus Group Innovations, Toulouse Cedex 03, France

    Jean-Claude Roussel

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Luzeaux, D. (2015). A Formal Foundation of Systems Engineering. In: Boulanger, F., Krob, D., Morel, G., Roussel, JC. (eds) Complex Systems Design & Management. Springer, Cham. https://doi.org/10.1007/978-3-319-11617-4_10

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  • DOI: https://doi.org/10.1007/978-3-319-11617-4_10

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-11616-7

  • Online ISBN: 978-3-319-11617-4

  • eBook Packages: EngineeringEngineering (R0)

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