Bulletin of Mathematical Biology

, Volume 39, Issue 2, pp 249–258 | Cite as

A logical model of genetic activities in Lukasiewicz algebras: The non-linear theory

  • I. C. Bâianu
  • M. Inst. P.


A categorical framework for logical models of functional genetic systems is proposed. The logical models of genetic nets are shown to simulate non-linear systems withn-state components and allow for the generalization of previous logical models of neural nets. An algebraic formulation of variable ‘next-state functions’ is presented which can be used for the description of developmental processes.


Turing Machine Projective Limit Categorical Framework Genetic Activity Predicate Expression 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Baianu, I. 1970. “Organismic Supercategories: II. On Multistable Systems.”Bull. Math. Biophys., 32, 539–561.MATHMathSciNetGoogle Scholar
  2. Baianu, I. 1971. “Organismic Supercategories and Qualitative Dynamics of Systems.” —Ibid.,33, 339–353.MATHGoogle Scholar
  3. Baianu, I. 1973. “Some Algebraic Properties of (M, R)-Systems.”Bull. Math. Biol.,35, 213–217.MATHMathSciNetCrossRefGoogle Scholar
  4. Carnap, R. 1938. “The Logical Syntax of Language.” New York: Harcourt, Brace and Co.Google Scholar
  5. Georgescu, G. and C. Vraciu. 1970. “On the Characterization of Lukasiewicz Algebras.”J. Algebra,16, 4, 486–495.MATHMathSciNetCrossRefGoogle Scholar
  6. Hilbert, D. and W. Ackerman. 1927.Gründuge der Theoretischen Log k. Berlin: Springer.Google Scholar
  7. Landahl, H. D., W. S. McCulloch and W. Pitts. 1943.Bull. Math. Biophys.,5, 135–137.MATHMathSciNetGoogle Scholar
  8. Löfgren, L. 1968. “An Axiomatic Explanation of Complete Self-Reproduction.”Bull. Math. Biophys.,30, 317–348.Google Scholar
  9. McCulloch, W. and W. Pitts. 1943. “A Logical Calculus of Ideas Immanent in Nervous Activity.” —Ibid.,5, 115–133.MATHMathSciNetGoogle Scholar
  10. Moisil, G. 1940. “Recherches sur les logiques non-chryssipiennes.”Annales scientifiques de l'Université de Jassy,26, 431–466.MATHMathSciNetGoogle Scholar
  11. Pitts, W. 1943. “The Linear Theory of Neuron Networks.”Bull. Math. Biophys.,5, 23–31.MATHMathSciNetGoogle Scholar
  12. Rashevsky, N. 1965. “The Representation of Organisms in Terms of Predicates.” —Ibid.,27, 477–491.Google Scholar
  13. Rashevsky, N. 1968. “Neurocybernetics as a Particular Case of General Regulating Mechanisms in Biological and Social Organisms.”Concepts de l'Age de la Science,3, 243–258.Google Scholar
  14. Rosen, R. 1958a. “A Relational Theory of Biological System.”Bull. Math. Biophys.,20, 245–260.MathSciNetGoogle Scholar
  15. Rosen, R. 1958b. “The Representation of Biological Systems form the Standpoint of the Theory of Categories.”Bull. Math. Biophys.,20, 317–341.MathSciNetGoogle Scholar
  16. Rosen, R. 1970.Dynamical Systems in Biology. A 2-volume Text-Monograph, vol. 1, New York: John Wiley & Sons, Inc. Ch. 8. pp. 236–249.Google Scholar
  17. Russel, Bertrand and A. N. Whitehead, 1925.Principia Mathematica, Cambridge: Cambridge Univ. Press.MATHGoogle Scholar

Copyright information

© Society for Mathematical Biology 1977

Authors and Affiliations

  • I. C. Bâianu
    • 1
  • M. Inst. P.
    • 1
  1. 1.Faculty of PhysicsBucharest-MâgureleRomania

Personalised recommendations