Skip to main content

Towards a Process Algebra and Operator Theory for Learning System Objects

  • Conference paper
  • First Online:
Artificial General Intelligence (AGI 2024)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 14951))

Included in the following conference series:

  • 746 Accesses

Abstract

Recently, abstract systems theory has been used as a meta-theory for learning theory and machine learning in order to model learning systems directly as formal, mathematical objects. This effort was inspired by a desire to treat learning in terms of systems, as opposed to the more common practice of treating learning in terms of problems or problem-solving, by modeling learning as a relation on sets, that is, as an abstract system. Such a relational view of learning, however, is heavily structural. It neglects key behavioral aspects typically represented using operators and process algebra. This paper substantiates and motivates the development of a process algebra for learning systems in order to address this gap. In summary, this paper considers and distinguishes formal representations of learning as a problem, as a system, as an operator, and as a process.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Notes

  1. 1.

    As quoted in Pan and Yang [18].

  2. 2.

    The transferred knowledge \(K_S\) is defined herein to be \(D_S\) and \(\varTheta _S\), the source data and parameters, following convention [18], however, in general, it could be comprised of any component set from \(S_S\).

References

  1. Bakirtzis, G., Fleming, C.H., Vasilakopoulou, C.: Categorical semantics of cyber-physical systems theory. ACM Trans. Cyber Phys. Syst. 5(3), 1–32 (2021)

    Article  Google Scholar 

  2. Belenchia, M., Thórisson, K.R., Eberding, L.M., Sheikhlar, A.: Elements of task theory. In: Goertzel, B., Iklé, M., Potapov, A. (eds.) AGI 2021. LNCS (LNAI), vol. 13154, pp. 19–29. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-93758-4_3

    Chapter  Google Scholar 

  3. Ben-David, S., Blitzer, J., Crammer, K., Pereira, F.: Analysis of representations for domain adaptation. Adv. Neural Inform. Proc. Syst. 19 (2006)

    Google Scholar 

  4. Bengio, Y., Louradour, J., Collobert, R., Weston, J.: Curriculum learning. In: Proceedings of the 26th Annual International Conference on Machine Learning, pp. 41–48 (2009)

    Google Scholar 

  5. Bommasani, R., et al.: On the opportunities and risks of foundation models. arXiv preprint arXiv:2108.07258 (2021)

  6. Chollet, F.: On the measure of intelligence. arXiv preprint arXiv:1911.01547 (2019)

  7. Cody, T.: Mesarovician abstract learning systems. In: Goertzel, B., Iklé, M., Potapov, A. (eds.) AGI 2021. LNCS (LNAI), vol. 13154, pp. 55–64. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-93758-4_7

    Chapter  Google Scholar 

  8. Cody, T.: Homomorphisms between transfer, multi-task, and meta-learning systems. In: Goertzel, B., Iklé, M., Potapov, A., Ponomaryov, D. (eds.) AGI 2022. LNCS (LNAI), pp. 199–208. Springer, Cham (2023). https://doi.org/10.1007/978-3-031-19907-3_19

    Chapter  Google Scholar 

  9. Cody, T., Adams, S., Beling, P.: Motivating a systems theory of AI. Insight 23(1), 37–40 (2020)

    Article  Google Scholar 

  10. Cody, T., Adams, S., Beling, P.A.: A systems theoretic perspective on transfer learning. In: 2019 IEEE International Systems Conference (SysCon), pp. 1–7. IEEE (2019)

    Google Scholar 

  11. Cody, T., Beling, P.A.: A systems theory of transfer learning. IEEE Syst. J. 17(1), 26–37 (2023)

    Article  Google Scholar 

  12. De Nicola, R.: Process Algebras. In: Padua, D. (eds) Encyclopedia of Parallel Computing. Springer, Boston, MA (2011). https://doi.org/10.1007/978-0-387-09766-4_450

  13. Gilmore, S., Hillston, J.: The PEPA workbench: a tool to support a process algebra-based approach to performance modelling. In: Haring, G., Kotsis, G. (eds.) TOOLS 1994. LNCS, vol. 794, pp. 353–368. Springer, Heidelberg (1994). https://doi.org/10.1007/3-540-58021-2_20

    Chapter  Google Scholar 

  14. Meredith, L.G., Radestock, M.: A reflective higher-order calculus. Electron. Notes Theoret. Comput. Sci. 141(5), 49–67 (2005)

    Article  Google Scholar 

  15. Mesarovic, M.D., Takahara, Y. (eds.): Abstract Systems Theory. Springer, Berlin, Heidelberg (1989)

    Google Scholar 

  16. Mitchell, T., et al.: Never-ending learning. Commun. ACM 61(5), 103–115 (2018)

    Article  Google Scholar 

  17. Nivel, E., et al.: Bounded seed-AGI. In: Goertzel, B., Orseau, L., Snaider, J. (eds.) AGI 2014. LNCS (LNAI), vol. 8598, pp. 85–96. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09274-4_9

    Chapter  Google Scholar 

  18. Pan, S.J., Yang, Q.: A survey on transfer learning. IEEE Trans. Knowl. Data Eng. 22(10), 1345–1359 (2009)

    Article  Google Scholar 

  19. du Preez, A., Beling, P., Cody, T.: A systems theoretic approach to online machine learning. In: 2024 IEEE International Systems Conference (SysCon), pp. 1–8. IEEE (2024)

    Google Scholar 

  20. Thórisson, K.R.: A new constructivist AI: from manual methods to self-constructive systems. In: Wang, P., Goertzel, B. (eds.) Theoretical Foundations of Artificial General Intelligence, pp. 145–171. Atlantis Press, Paris (2012). https://doi.org/10.2991/978-94-91216-62-6_9

    Chapter  Google Scholar 

  21. Thórisson, K.R.: Seed-programmed autonomous general learning. In: International Workshop on Self-Supervised Learning, pp. 32–61. PMLR (2020)

    Google Scholar 

  22. Thórisson, K.R., Bieger, J., Thorarensen, T., Sigurðardóttir, J.S., Steunebrink, B.R.: Why artificial intelligence needs a task theory. In: Steunebrink, B., Wang, P., Goertzel, B. (eds.) AGI -2016. LNCS (LNAI), vol. 9782, pp. 118–128. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-41649-6_12

    Chapter  Google Scholar 

  23. Wang, Y.: Using process algebra to describe human and software behaviors. Brain Mind 4, 199–213 (2003)

    Article  Google Scholar 

  24. Wang, Y.: Deductive semantics of RTPA. IJCINI 2(2), 95–121 (2008)

    Google Scholar 

  25. Weinshall, D., Cohen, G., Amir, D.: Curriculum learning by transfer learning: theory and experiments with deep networks. In: International Conference on Machine Learning, pp. 5238–5246. PMLR (2018)

    Google Scholar 

  26. Weiss, K., Khoshgoftaar, T.M., Wang, D.: A survey of transfer learning. J. Big Data 3, 1–40 (2016)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Tyler Cody .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Cody, T., Beling, P.A. (2024). Towards a Process Algebra and Operator Theory for Learning System Objects. In: Thórisson, K.R., Isaev, P., Sheikhlar, A. (eds) Artificial General Intelligence. AGI 2024. Lecture Notes in Computer Science(), vol 14951. Springer, Cham. https://doi.org/10.1007/978-3-031-65572-2_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-65572-2_5

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-65571-5

  • Online ISBN: 978-3-031-65572-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics