Genetic `nets', or networks- that form a living organism's genome -are mathematical models of functional genes linked via their non-linear, dynamic interactions. The simpler, Boolean, or two-state models of genomes form a proper subcategory of the category of n-state genetic networks, that operate on the basis of a Łukasiewicz-Moisil n-valued logic algebra . Then, the category of genetic networks, was shown in ref. [2] to form a subcategory of the algebraic category of Łukasiewicz algebras, [1,2]. Furthermore, the category of automata (or sequential machines based on Chrysippean or Boolean logic) and the category of -systems (that can be realized as concrete metabolic-repair biosystems of enzymes, genes, and so on) are subcategories of . The latter corresponds to organismic sets of zero-th order in the simpler, Rashevsky's theory of organismic sets.

Bibliography

1

Baianu, I.C. (1977). A Logical Model of Genetic Activities in Łukasiewicz Algebras: The Non-linear Theory., Bulletin of Mathematical Biology, 39:249-258.

2

Baianu, I.C., Brown, R., Georgescu, G., Glazebrook, J.F. (2006). Complex nonlinear biodynamics in categories, higher dimensional algebra and Łukasiewicz-Moisil topos: transformations of neuronal, genetic and neoplastic networks. Axiomathes 16(1-2):65-122.

3

Baianu, I.C., J. Glazebrook, G. Georgescu and R.Brown. (2008). A Novel Approach to Complex Systems Biology based on Categories, Higher Dimensional Algebra and Łukasiewicz Topos. Manuscript in preparation, 16 pp.

4

Georgescu, G. and C. Vraciu (1970). On the Characterization of Łukasiewicz Algebras., J. Algebra, 16 (4), 486-495.