Multi-valued logic in graph transformation theory and self-adaptive systems

  • Dmitry MaximovEmail author
  • Sergey Ryvkin


Graph transformation theory uses rules to perform a graph transformation. However, there is no a way to choose between such different transformations in the case where several of them are applicable. A way to get the choice is suggested here based on the comparing of the values of implications which correspond to different transformation variants. The relationship between the topos of bundles, and the set of graphs with the same vertices, is introduced to include logic into graph transformation theory. Thus, one can use the special type of implication and the truth-values set of such a topos to estimate different variants of graph transformations. In this approach, the maximal part of the initial graph towards the terminal one is conserved in the chosen variant. Analysis of self-adaptive systems uses some graph grammars. Self-adaptive systems autonomously perform an adaptation to changes both in user needs and in their operational environments, while still maintaining some desired properties. The suggested way to choose such graph transformation variants may be used to make a choice between different graph grammars in such systems modeling. This approach is illustrated in a model of some business processes, that result in the automated choice of the business process adaptation under the assumption that the process changes are minimal towards the terminal state.


Multi-valued logic Decision making Graph transformation Self-adaptive systems 

Mathematics Subject Classification (2010)

03B70 68T27 68R10 68T05 68U35 


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The project was partly supported by RFBR grant 16-08-00832a.


  1. 1.
    Aizerman, M., Aleskerov, F.: Choice of variants (foundations of the theory). Nauka, Moscow (1990)Google Scholar
  2. 2.
    Angelis, F.L.D., Serugendo, G.D.M., Szalas, A.: Paraconsistent rule-based reasoning with graded truth values. J. Appl. Log. 5(1), 185–220 (2018)MathSciNetGoogle Scholar
  3. 3.
    Bencomo, N., Gëotz, S., et al.: Models@Run.Time: a guided tour of the state of the art and research challenges. In: Software & Systems Modeling (2019)Google Scholar
  4. 4.
    Birkhoff, G.: Lattice theory. Providence, Rhode Island (1967)zbMATHGoogle Scholar
  5. 5.
    Böse, F., Piotrowski, J., Scholz-Reiter, B.: Autonomously controlled storage management in vehicle logistics - applications of RFID and mobile computing systems. Int. Journal of RT Technologies: Research an Application 1(1), 57–76 (2009)CrossRefGoogle Scholar
  6. 6.
    Brun, Y., Serugendo, G.D.M., Gacek, C., et al.: Engineering self-adaptive systems through feedback loops. In: Software Engineering for Self-Adaptive Systems, pp 48–70 (2009)CrossRefGoogle Scholar
  7. 7.
    Bucchiarone, A., Ehrig, H., Ermel, C., et al.: Modelling and analysis of self-adapting systems based on graph transformation. Technical Report 2013/03, TU Berlin, (2013)
  8. 8.
    Bucchiarone, A., Ehrig, H., Ermel, C., et al.: Rule-based modeling and static analysis of self-adaptive systems by graph transformation. LNCS 8950, 582–601 (2015)zbMATHGoogle Scholar
  9. 9.
    D’Angelo, M., Gerasimou, S., Ghahremani, S., et al.: On learning in collective self-adaptive systems: state of practice and a 3D framework. Preprint, (2019)
  10. 10.
    Ehrig, H., Ehrig, K., Prange, U., et al.: Fundamentals of algebraic graph transformations. Springer, Berlin (2006)zbMATHGoogle Scholar
  11. 11.
    Ehrig, H., Padberg, J.: Graf grammars and petri net transformations. LNCS 3098, 496–536 (2004)zbMATHGoogle Scholar
  12. 12.
    Goldblatt, R.: Topoi. The categorial analysis of logic. N.-H. Pub. Co., Amsterdam (1979)zbMATHGoogle Scholar
  13. 13.
    Jiménez, M., Rivera, L.F., Villegas, N., et al.: An architectural framework for quality-driven adaptive continuous experimentation. In: 2019 IEEE/ACM Joint 4th International Workshop on Rapid Continuous Software Engineering and 1st International Workshop on Data-Driven Decisions, Experimentation and Evolution. (2019)
  14. 14.
    Lawvere, F.W.: Qualitative distinctions between some toposes of generalized graphs. In: Categories in Computer Science and Logic. Contemporary Mathematics, vol. 92. Amer. Math. Soc. (1989)Google Scholar
  15. 15.
    Mahfoudh, H.B., Serugendo, G.D.M., Boulmier, A., Abdennadher, N.: Coordination model with reinforcement learning for ensuring reliable on-demand services in collective adaptive systems. In: Proceedings of the 8th International Symposium, ISoLA 2018, Part III. (2018)CrossRefGoogle Scholar
  16. 16.
    Maksimov, D.Y.: Reconfiguring system hierarchies with multi–valued logic. Autom. Remote. Control. 77(3), 462–472 (2016)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Maximov, D.: N.A. Vasil’ev’s logic and many-valued logics. Logical Investigations 22(1), 82–107 (2016)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Maximov, D.: N. Vasiliev’s logic ideas and the categorical semantics of manyvalued logic. Logica Universalis 10(1), 21–43 (2016)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Maximov, D.: A tool for linear logic structure calculating and decision making in a robot group in preparing (2019)Google Scholar
  20. 20.
    Maximov, D.Y., Legovich, Y.S., Ryvkin, S.E.: How the structure of system problems influences system behavior. Autom. Remote. Control. 78(4), 689–699 (2017)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Sabatucci, L., Seidita, V., Cossentino, M.: The four types of self-adaptive systems: a metamodel. In: Smart Innovation.
  22. 22.
    Salehie, M., Tahvildari, L.: Self-adaptive software: Landscape and research challenges. ACM Trans. Auton. 4(2), 14:1–14:42 (2009)Google Scholar
  23. 23.
    Solano, G.F., Caldas, R.D., Rodrigues, G.N., et al.: A learning approach to enhance assurances for real-time self-adaptive systems. In: Proceedings of the 13-th International Conference on Software Engineering for Adaptive and Self-Managing Systems, Ser. SEAMS., pp 206–216. ACM (2018)
  24. 24.
    Solano, G.F., Caldas, R.D., Rodrigues, G.N., et al.: Taming uncertainty in the assurance process of self-adaptive systems: a goal- oriented approach. Preprint, (2019)
  25. 25.
    Villegas, N., Tamura, G., Müller, H.A.: Architecting software systems for runtime self-adaptation. In: Managing Trade-Offs in Adaptable Software Architectures. Amer. Math. Soc. (2017)CrossRefGoogle Scholar
  26. 26.
    Weyns, D.: Software engineering of self-adaptive systems: an organised tour and future challenges. In: Kang, K.K.C., Cha, S. (eds.) Handbook of Software Engineering. Springer (2017)Google Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Trapeznikov Institute of Control Science Russian Academy of SciencesMoscowRussia

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