Abstract
There have recently been some computational or mathematical formalization studies on closedness of living systems such as autopoiesis and (M,R) systems. In particular, some have mentioned relationships between cartesian closed categories and λ–calculus. Following this line, the paper proposes a framework to formalize autopoiesis by combining category theory and λ–calculus more strictly, by introducing an equivalence between the category of cartesian closed categories and that of λ–calculi while providing a formalization of the distinction between organization and structure in autopoietic systems.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Bourgine, P., Stewart, J.: Autopoiesis and cognition. Artificial Life 10(3), 327–346 (2004)
Cárdenas, M.L., Letelier, J.C., Gutierrez, C., Cornish-Bowden, A., Soto-Andrade, J.: Closure to efficient causation, computability and artificial life. Journal of Theoretical Biology 263, 79–92 (2010)
Chemero, A., Turvey, M.T.: Complexity and ”closure to efficient cause”. In: Proc. AlifeX: Workshiop on Artificial Autonomy, pp. 13–19 (2006)
Egbert, M.D., Di Paolo, E.: Integrating autopoiesis and behavior: An exploration in computational chemo–ethology. Adaptive Behavior 17(5), 387–401 (2009)
Kampis, G.: Self–Modifying Systems in Biology and Cognitive Science: A New Framework for Synamics. Pergamon Press (1991)
Lambek, J., Scott, P.J.: Introduction to Higher Order Categorical Logic. Cambridge University Press (1986)
Letelier, J.C., Soto-Andrade, J., Abarzúa, F.G., Cornish-Bowden, A., Cárdenas, M.L.: Organizational invariance and metabolic closure: Analysis in terms of (M,R) systems. Journal of Theoretical Biology 238, 949–961 (2006)
Maturana, H.R., Varela, F.J.: Autopoiesis and Cognition: The Realization of the Living. D. Reidel Publishing (1980)
Maturana, H.R., Varela, F.J.: The Tree of Knowledge. Shambala Publications (1987)
McMullin, B.: Thirty years of computational autopoiesis. Artificial Life 10(3), 277–296 (2004)
Mossio, M., Longo, G., Stewart, J.: A computable expression of closure to efficient causation. Journal of Theoretical Biology 257(3), 489–498 (2009)
Nomura, T.: Category theoretical formalization of autopoieis from perspective of distinction between organization and structure. In: Proc. Seventh German Workshop on Artificial Life, pp. 31–38 (2006)
Nomura, T.: Category Theoretical Distinction between Autopoiesis and (M,R) Systems. In: Almeida e Costa, F., Rocha, L.M., Costa, E., Harvey, I., Coutinho, A. (eds.) ECAL 2007. LNCS (LNAI), vol. 4648, pp. 465–474. Springer, Heidelberg (2007)
Rosen, R.: Life Itself. Columbia University Press (1991)
Soto-Andrade, J., Varela, F.J.: Self–reference and fixed points: A discussion and an extension of Lawvere’s theorem. Acta Applicandae Mathematicae 2, 1–19 (1984)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag GmbH Berlin Heidelberg
About this chapter
Cite this chapter
Nomura, T. (2012). A Proposal for Combination of Category Theory and λ–Calculus in Formalization of Autopoiesis. In: Simeonov, P., Smith, L., Ehresmann, A. (eds) Integral Biomathics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28111-2_12
Download citation
DOI: https://doi.org/10.1007/978-3-642-28111-2_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-28110-5
Online ISBN: 978-3-642-28111-2
eBook Packages: EngineeringEngineering (R0)