1 Fuzzy logics of living organisms
Living organisms or biosystems can be represented as super-complex systems with dynamics that is
not reducible to that of their components, such as molecules and atoms. It is an empirically
accepted fact that living organisms exhibit a wide degree of “biological variability”: genetic,
epigenetic, phenotypic, and metabolic variability within the same species. Their behavior and
dynamics thus exhibit a type of “fuzziness” (refs. [2, 3]) that, unlike Zadeh’s fuzzy sets
characteristic [7, 8], is neither random nor always described by a symmetric Gaussian
distribution.
It has been proposed that the operational logics underlying super-complex systems dynamics are
LMn many-valued logics for both genetic and neural networks (refs. [3, 6]).
References
[1] G. Georgescu, N-valued Logics and Łukasiewicz–Moisil Algebras, Axiomathes,
16(1–2), 123–136 (2006).
[2] I. C. Baianu and M. Marinescu, Organismic Supercategories: Towards a Unitary
Theory of Systems, Bulletin of Mathematical Biophysics, 30, 148–159 (1968).
[3] I. C. Baianu, A Logical Model of Genetic Activities in Łukasiewicz Algebras: The
Non-linear Theory, Bulletin of Mathematical Biology, 39, 249–258 (1977).
[4] I. C. Baianu, Computer Models and Automata Theory in Biology and Medicine, in
M. Witten (ed.), Mathematical Models in Medicine, vol. 7, ch. 11, Pergamon Press, New
York, 1513–1577 (1986–1987). CERN Preprint No. EXT-2004-072 and HTML abstract.
[5] I. C. Baianu, Molecular Models of Genetic and Organismic Structures, in
Proceedings of the Relational Biology Symposium, Argentina (1987). CERN Preprint
No. EXT-2004-067.
[6] I. C. Baianu, Łukasiewicz-Topos Models of Neural Networks, Cell Genome and
Interactome Nonlinear Dynamic Models (2004), e-print at Cogprints, Sussex University.
[7] L. A. Zadeh, Fuzzy Sets, Information and Control, 8, 338–353 (1965).
[8] L. A. Zadeh, The Concept of a Linguistic Variable and Its Application to
Approximate Reasoning I, II, III, Information Sciences, vols. 8–9 (1975), 199–249,
301–357, 43–80.
