%A Professor I.C. Baianu %A Professor George Georgescu %A Professor James F. Glazebrook %O http://www.edusoft.ro/brain/index.php/brain/article/view/97/201 ISSN: 2067-3957 %J Broad Research in Artifical Intelligence and Neuroscience %T ?ukasiewicz-Moisil Many-Valued Logic Algebra of Highly-Complex Systems %X A novel approach to self-organizing, highly-complex systems (HCS), such as living organisms and artificial intelligent systems (AIs), is presented which is relevant to Cognition, Medical Bioinformatics and Computational Neuroscience. Quantum Automata (QAs) were defined in our previous work as generalized, probabilistic automata with quantum state spaces (Baianu, 1971). Their next-state functions operate through transitions between quantum states defined by the quantum equations of motion in the Schroedinger representation, with both initial and boundary conditions in space-time. Such quantum automata operate with a quantum logic, or Q-logic, significantly different from either Boolean or ?ukasiewicz many-valued logic. A new theorem is proposed which states that the category of quantum automata and automata--homomorphisms has both limits and colimits. Therefore, both categories of quantum automata and classical automata (sequential machines) are bicomplete. A second new theorem establishes that the standard automata category is a subcategory of the quantum automata category. The quantum automata category has a faithful representation in the category of Generalized (M,R)--Systems which are open, dynamic biosystem networks with defined biological relations that represent physiological functions of primordial organisms, single cells and higher organisms. %N 1-2 %K LM--algebraic logic, LM--logic algebras, algebraic category of LM-logic algebras, fundamental theorems of LM-logic algebra, non-linear genetic networks, nonlinear dynamics, Epigenomics, Cellular Interactomics, Immunology and hormonal regulatory systems, category theory, functors and natural transformations, toposes and Heyting logic algebras, quantum automata categories, limits and colimits, quantum automata homomorphisms, Abelian category, bicomplete categories, Quantum Relational Biology, generalised metabolic-replication, (M,R)--systems, complex bionetworks, quantum logic, non-commutative lattices, Hilbert space, quantum computers, computability of complex biological systems, Cartesian closed categories, extended quantum topos, category of groupoids, dynamic realisations of generalised (M,R)-systems (GMRs), category of GMRs, compact subsystems of GMR %P 1-11 %E Dr. Barna Iantovics %V 1 %D 2010 %I BRAIN %L cogprints7751